diff --git a/tests/opt-testcases/tls13-compat.sh b/tests/opt-testcases/tls13-compat.sh
index a1bb526526..291fe1c44d 100755
--- a/tests/opt-testcases/tls13-compat.sh
+++ b/tests/opt-testcases/tls13-compat.sh
@@ -3475,48 +3475,14 @@ run_test "TLS 1.3 m->G: TLS_AES_128_CCM_8_SHA256,x448,rsa_pss_rsae_sha256" \
          -c "Verifying peer X.509 certificate... ok" \
          -C "received HelloRetryRequest message"
 
-requires_openssl_tls1_3
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
-requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-run_test "TLS 1.3 m->O: HRR secp384r1 -> secp256r1" \
-         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-256 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp256r1" \
-         0 \
-         -c "HTTP/1.0 200 ok" \
-         -c "NamedGroup: secp384r1 ( 18 )" \
-         -c "NamedGroup: secp256r1 ( 17 )" \
-         -c "Verifying peer X.509 certificate... ok" \
-         -c "received HelloRetryRequest message" \
-         -c "selected_group ( 23 )"
-
-requires_gnutls_tls1_3
-requires_gnutls_next_no_ticket
-requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
-requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-run_test "TLS 1.3 m->G: HRR secp384r1 -> secp256r1" \
-         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP256R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp256r1" \
-         0 \
-         -c "HTTP/1.0 200 OK" \
-         -c "NamedGroup: secp384r1 ( 18 )" \
-         -c "NamedGroup: secp256r1 ( 17 )" \
-         -c "Verifying peer X.509 certificate... ok" \
-         -c "received HelloRetryRequest message" \
-         -c "selected_group ( 23 )"
-
 requires_openssl_tls1_3
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 run_test "TLS 1.3 m->O: HRR secp256r1 -> secp384r1" \
-         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp384r1.crt -key data_files/ecdsa_secp384r1.key -accept $SRV_PORT -groups P-384 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp384r1_sha384 curves=secp256r1,secp384r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-384 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,secp384r1" \
          0 \
          -c "HTTP/1.0 200 ok" \
          -c "NamedGroup: secp256r1 ( 17 )" \
@@ -3525,32 +3491,14 @@ run_test "TLS 1.3 m->O: HRR secp256r1 -> secp384r1" \
          -c "received HelloRetryRequest message" \
          -c "selected_group ( 24 )"
 
-requires_gnutls_tls1_3
-requires_gnutls_next_no_ticket
-requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
-requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-run_test "TLS 1.3 m->G: HRR secp256r1 -> secp384r1" \
-         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp384r1.crt --x509keyfile data_files/ecdsa_secp384r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP384R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp384r1_sha384 curves=secp256r1,secp384r1" \
-         0 \
-         -c "HTTP/1.0 200 OK" \
-         -c "NamedGroup: secp256r1 ( 17 )" \
-         -c "NamedGroup: secp384r1 ( 18 )" \
-         -c "Verifying peer X.509 certificate... ok" \
-         -c "received HelloRetryRequest message" \
-         -c "selected_group ( 24 )"
-
 requires_openssl_tls1_3
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 run_test "TLS 1.3 m->O: HRR secp256r1 -> secp521r1" \
-         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp521r1.crt -key data_files/ecdsa_secp521r1.key -accept $SRV_PORT -groups P-521 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp521r1_sha512 curves=secp256r1,secp521r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-521 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,secp521r1" \
          0 \
          -c "HTTP/1.0 200 ok" \
          -c "NamedGroup: secp256r1 ( 17 )" \
@@ -3559,33 +3507,14 @@ run_test "TLS 1.3 m->O: HRR secp256r1 -> secp521r1" \
          -c "received HelloRetryRequest message" \
          -c "selected_group ( 25 )"
 
-requires_gnutls_tls1_3
-requires_gnutls_next_no_ticket
-requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
-requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-run_test "TLS 1.3 m->G: HRR secp256r1 -> secp521r1" \
-         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp521r1.crt --x509keyfile data_files/ecdsa_secp521r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP521R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp521r1_sha512 curves=secp256r1,secp521r1" \
-         0 \
-         -c "HTTP/1.0 200 OK" \
-         -c "NamedGroup: secp256r1 ( 17 )" \
-         -c "NamedGroup: secp521r1 ( 19 )" \
-         -c "Verifying peer X.509 certificate... ok" \
-         -c "received HelloRetryRequest message" \
-         -c "selected_group ( 25 )"
-
 requires_openssl_tls1_3
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
 requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
 run_test "TLS 1.3 m->O: HRR secp256r1 -> x25519" \
-         "$O_NEXT_SRV_NO_CERT -cert data_files/server2-sha256.crt -key data_files/server2.key -accept $SRV_PORT -groups X25519 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca_cat12.crt sig_algs=rsa_pss_rsae_sha256 curves=secp256r1,x25519" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X25519 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,x25519" \
          0 \
          -c "HTTP/1.0 200 ok" \
          -c "NamedGroup: secp256r1 ( 17 )" \
@@ -3594,25 +3523,6 @@ run_test "TLS 1.3 m->O: HRR secp256r1 -> x25519" \
          -c "received HelloRetryRequest message" \
          -c "selected_group ( 29 )"
 
-requires_gnutls_tls1_3
-requires_gnutls_next_no_ticket
-requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
-requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
-requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
-run_test "TLS 1.3 m->G: HRR secp256r1 -> x25519" \
-         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key --priority=NONE:+CIPHER-ALL:+GROUP-X25519:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
-         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca_cat12.crt sig_algs=rsa_pss_rsae_sha256 curves=secp256r1,x25519" \
-         0 \
-         -c "HTTP/1.0 200 OK" \
-         -c "NamedGroup: secp256r1 ( 17 )" \
-         -c "NamedGroup: x25519 ( 1d )" \
-         -c "Verifying peer X.509 certificate... ok" \
-         -c "received HelloRetryRequest message" \
-         -c "selected_group ( 29 )"
-
 requires_openssl_tls1_3
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
@@ -3629,6 +3539,316 @@ run_test "TLS 1.3 m->O: HRR secp256r1 -> x448" \
          -c "received HelloRetryRequest message" \
          -c "selected_group ( 30 )"
 
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp384r1 -> secp256r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-256 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp384r1 -> secp521r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-521 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp384r1 -> x25519" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X25519 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,x25519" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp384r1 -> x448" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X448 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,x448" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp521r1 -> secp256r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-256 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp521r1 -> secp384r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-384 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp521r1 -> x25519" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X25519 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,x25519" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR secp521r1 -> x448" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X448 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,x448" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x25519 -> secp256r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-256 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x25519 -> secp384r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-384 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x25519 -> secp521r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-521 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x25519 -> x448" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X448 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,x448" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x448 -> secp256r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-256 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x448 -> secp384r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-384 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x448 -> secp521r1" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups P-521 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->O: HRR x448 -> x25519" \
+         "$O_NEXT_SRV_NO_CERT -cert data_files/ecdsa_secp256r1.crt -key data_files/ecdsa_secp256r1.key -accept $SRV_PORT -groups X25519 -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,x25519" \
+         0 \
+         -c "HTTP/1.0 200 ok" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp256r1 -> secp384r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP384R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp256r1 -> secp521r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP521R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp256r1 -> x25519" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X25519:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp256r1,x25519" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
 requires_gnutls_tls1_3
 requires_gnutls_next_no_ticket
 requires_gnutls_next_disable_tls13_compat
@@ -3646,3 +3866,291 @@ run_test "TLS 1.3 m->G: HRR secp256r1 -> x448" \
          -c "Verifying peer X.509 certificate... ok" \
          -c "received HelloRetryRequest message" \
          -c "selected_group ( 30 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp384r1 -> secp256r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP256R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp384r1 -> secp521r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP521R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp384r1 -> x25519" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X25519:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,x25519" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp384r1 -> x448" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X448:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp384r1,x448" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp521r1 -> secp256r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP256R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp521r1 -> secp384r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP384R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp521r1 -> x25519" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X25519:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,x25519" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR secp521r1 -> x448" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X448:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=secp521r1,x448" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x25519 -> secp256r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP256R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x25519 -> secp384r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP384R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x25519 -> secp521r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP521R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x25519 -> x448" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X448:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x25519,x448" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 30 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x448 -> secp256r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP256R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp256r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp256r1 ( 17 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 23 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x448 -> secp384r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP384R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp384r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp384r1 ( 18 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 24 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x448 -> secp521r1" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-SECP521R1:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,secp521r1" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: secp521r1 ( 19 )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 25 )"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test "TLS 1.3 m->G: HRR x448 -> x25519" \
+         "$G_NEXT_SRV_NO_CERT --http --disable-client-cert --debug=4 --x509certfile data_files/ecdsa_secp256r1.crt --x509keyfile data_files/ecdsa_secp256r1.key --priority=NONE:+CIPHER-ALL:+GROUP-X25519:+MAC-ALL:+SIGN-ALL:+VERS-TLS1.3:%NO_TICKETS" \
+         "$P_CLI server_addr=127.0.0.1 server_port=$SRV_PORT debug_level=4 force_version=tls13 ca_file=data_files/test-ca2.crt sig_algs=ecdsa_secp256r1_sha256 curves=x448,x25519" \
+         0 \
+         -c "HTTP/1.0 200 OK" \
+         -c "NamedGroup: x448 ( 1e )" \
+         -c "NamedGroup: x25519 ( 1d )" \
+         -c "Verifying peer X.509 certificate... ok" \
+         -c "received HelloRetryRequest message" \
+         -c "selected_group ( 29 )"
diff --git a/tests/scripts/generate_tls13_compat_tests.py b/tests/scripts/generate_tls13_compat_tests.py
index 63993459a6..fdc0c6d8ed 100755
--- a/tests/scripts/generate_tls13_compat_tests.py
+++ b/tests/scripts/generate_tls13_compat_tests.py
@@ -251,7 +251,7 @@ class GnuTLSServ(TLSProgram):
             priority_string_list.extend(update_priority_string_list(
                 signature_algorithms, self.SIGNATURE_ALGORITHM))
         else:
-            priority_string_list.extend(['SIGN-ALL','MAC-ALL'])
+            priority_string_list.extend(['SIGN-ALL', 'MAC-ALL'])
 
 
         if self._named_groups:
@@ -375,24 +375,19 @@ def generate_compat_test(server=None, client=None, cipher=None, sig_alg=None, na
     return '\n'.join(server_object.pre_checks() + client_object.pre_checks() + [cmd])
 
 
-def generate_hrr_compat_test(server=None, client=None, cipher=None, sig_alg=None,
-                             server_named_group=None):
+def generate_hrr_compat_test(client=None, server=None, cert_sig_alg=None,
+                             client_named_group=None, server_named_group=None):
     """
     Generate Hello Retry Request test case with `ssl-opt.sh` format.
     """
-    # Get a named_group for client side which does not equal input named_group
-    client_named_group = list(sorted(set(NAMED_GROUP_IANA_VALUE.keys() - {server_named_group})))[0]
     name = 'TLS 1.3 {client[0]}->{server[0]}: HRR {c_named_group} -> {s_named_group}'.format(
-            client=client, server=server, c_named_group=client_named_group,
-            s_named_group=server_named_group)
-    server_object = SERVER_CLASSES[server](ciphersuite=cipher,
-                                           named_group=server_named_group,
-                                           cert_sig_alg=sig_alg)
+        client=client, server=server, c_named_group=client_named_group,
+        s_named_group=server_named_group)
+    server_object = SERVER_CLASSES[server](named_group=server_named_group,
+                                           cert_sig_alg=cert_sig_alg)
 
-    client_object = CLIENT_CLASSES[client](ciphersuite=cipher,
-                                           named_group=client_named_group,
-                                           cert_sig_alg=sig_alg)
-    # after here, the named_group order is client_named_group, named_group.
+    client_object = CLIENT_CLASSES[client](named_group=client_named_group,
+                                           cert_sig_alg=cert_sig_alg)
     client_object.add_named_groups(server_named_group)
 
     cmd = ['run_test "{}"'.format(name), '"{}"'.format(
@@ -438,12 +433,6 @@ SSL_OUTPUT_HEADER = '''#!/bin/sh
 #
 '''
 
-def cycle_zip(*iters, max_len=None):
-    max_len = max_len or max([len(i) for i in iters])
-    cycle_iters = zip(*[itertools.cycle(i) for i in iters])
-    for _, c in zip(range(max_len), cycle_iters):
-        yield c
-
 def main():
     """
     Main function of this program
@@ -501,15 +490,16 @@ def main():
                                        server=server, client=client)
 
         # Generate Hello Retry Request  compat test cases
-        for combine_fields, server, client in \
-            itertools.product(list(cycle_zip(CIPHER_SUITE_IANA_VALUE.keys(),
-                                             SIG_ALG_IANA_VALUE.keys(),
-                                             NAMED_GROUP_IANA_VALUE.keys())),
+        for client, server, client_named_group, server_named_group in \
+            itertools.product(CLIENT_CLASSES.keys(),
                               SERVER_CLASSES.keys(),
-                              CLIENT_CLASSES.keys()):
-            cipher, sig_alg, named_group = combine_fields
-            yield generate_hrr_compat_test( server_named_group=named_group, sig_alg=sig_alg,
-                                           server=server, client=client)
+                              NAMED_GROUP_IANA_VALUE.keys(),
+                              NAMED_GROUP_IANA_VALUE.keys()):
+            if client_named_group != server_named_group:
+                yield generate_hrr_compat_test(client=client, server=server,
+                                               cert_sig_alg="ecdsa_secp256r1_sha256",
+                                               client_named_group=client_named_group,
+                                               server_named_group=server_named_group)
 
     if args.generate_all_tls13_compat_tests:
         if args.output: