diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 0d47fd5271..a51b49f11f 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -79,24 +79,20 @@ fi
 
 if [ -n "${OPENSSL_NEXT:-}" ]; then
     O_NEXT_SRV="$OPENSSL_NEXT s_server -www -cert data_files/server5.crt -key data_files/server5.key"
-    O_NEXT_SRV_RSA="$OPENSSL_NEXT s_server -www -cert data_files/server2-sha256.crt -key data_files/server2.key"
     O_NEXT_SRV_NO_CERT="$OPENSSL_NEXT s_server -www "
     O_NEXT_CLI="echo 'GET / HTTP/1.0' | $OPENSSL_NEXT s_client"
 else
     O_NEXT_SRV=false
-    O_NEXT_SRV_RSA=false
     O_NEXT_SRV_NO_CERT=false
     O_NEXT_CLI=false
 fi
 
 if [ -n "${GNUTLS_NEXT_SERV:-}" ]; then
     G_NEXT_SRV="$GNUTLS_NEXT_SERV --x509certfile data_files/server5.crt --x509keyfile data_files/server5.key"
-    G_NEXT_SRV_RSA="$GNUTLS_NEXT_SERV --x509certfile data_files/server2-sha256.crt --x509keyfile data_files/server2.key"
     G_NEXT_SRV_NO_CERT="$GNUTLS_NEXT_SERV"
 else
     G_NEXT_SRV=false
     G_NEXT_SRV_NO_CERT=false
-    G_NEXT_SRV_RSA=false
 fi
 
 if [ -n "${GNUTLS_NEXT_CLI:-}" ]; then
@@ -1444,14 +1440,12 @@ fi
 
 if [ -n "${OPENSSL_NEXT:-}" ]; then
     O_NEXT_SRV="$O_NEXT_SRV -accept $SRV_PORT"
-    O_NEXT_SRV_RSA="$O_NEXT_SRV_RSA -accept $SRV_PORT"
     O_NEXT_SRV_NO_CERT="$O_NEXT_SRV_NO_CERT -accept $SRV_PORT"
     O_NEXT_CLI="$O_NEXT_CLI -connect 127.0.0.1:+SRV_PORT"
 fi
 
 if [ -n "${GNUTLS_NEXT_SERV:-}" ]; then
     G_NEXT_SRV="$G_NEXT_SRV -p $SRV_PORT"
-    G_NEXT_SRV_RSA="$G_NEXT_SRV_RSA -p $SRV_PORT"
     G_NEXT_SRV_NO_CERT="$G_NEXT_SRV_NO_CERT -p $SRV_PORT"
 fi
 
@@ -8867,22 +8861,6 @@ run_test    "TLS1.3: minimal feature sets - openssl" \
             -c "<= parse finished message" \
             -c "HTTP/1.0 200 ok"
 
-requires_openssl_tls1_3
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
-requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
-run_test    "TLS 1.3 m->O AES_128_GCM_SHA256      , RSA_PSS_RSAE_SHA256" \
-            "$O_NEXT_SRV_RSA -ciphersuites TLS_AES_128_GCM_SHA256 -tls1_3 -msg -no_middlebox -num_tickets 0" \
-            "$P_CLI debug_level=4 force_version=tls13 server_name=localhost force_ciphersuite=TLS1-3-AES-128-GCM-SHA256 allow_sha1=0" \
-            0 \
-            -c "ECDH curve: x25519" \
-            -c "server hello, chosen ciphersuite: ( 1301 ) - TLS1-3-AES-128-GCM-SHA256" \
-            -c "Certificate Verify: Signature algorithm ( 0804 )" \
-            -c "mbedtls_ssl_tls13_process_certificate_verify() returned 0" \
-            -c "HTTP/1.0 200 ok"
-
 requires_gnutls_tls1_3
 requires_gnutls_next_no_ticket
 requires_gnutls_next_disable_tls13_compat
@@ -8915,24 +8893,6 @@ run_test    "TLS1.3: minimal feature sets - gnutls" \
             -c "<= parse finished message" \
             -c "HTTP/1.0 200 OK"
 
-requires_gnutls_next_no_ticket
-requires_gnutls_next_disable_tls13_compat
-requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL
-requires_config_enabled MBEDTLS_DEBUG_C
-requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_X509_RSASSA_PSS_SUPPORT
-requires_config_disabled MBEDTLS_USE_PSA_CRYPTO
-requires_gnutls_next
-run_test    "TLS 1.3 m->G AES_128_GCM_SHA256      , RSA_PSS_RSAE_SHA256" \
-            "$G_NEXT_SRV_RSA --disable-client-cert --priority=NORMAL:+CIPHER-ALL:+SHA256:+GROUP-SECP256R1:+ECDHE-ECDSA:+AEAD:+SIGN-RSA-PSS-RSAE-SHA256:-VERS-ALL:+VERS-TLS1.3:%NO_TICKETS:%DISABLE_TLS13_COMPAT_MODE" \
-            "$P_CLI debug_level=4 force_version=tls13 server_name=localhost force_ciphersuite=TLS1-3-AES-128-GCM-SHA256 allow_sha1=0" \
-            0 \
-            -c "ECDH curve: x25519"         \
-            -c "server hello, chosen ciphersuite: ( 1301 ) - TLS1-3-AES-128-GCM-SHA256" \
-            -c "Certificate Verify: Signature algorithm ( 0804 )" \
-            -c "mbedtls_ssl_tls13_process_certificate_verify() returned 0" \
-            -c "HTTP/1.0 200 OK"
-
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3_EXPERIMENTAL
 skip_handshake_stage_check
 requires_gnutls_tls1_3