diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index eefd89dd9b..a25a05c75e 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -4355,18 +4355,6 @@ static uint16_t ssl_preset_default_sig_algs[] = {
 #endif /* MBEDTLS_ECDSA_C && MBEDTLS_SHA384_C &&
           MBEDTLS_ECP_DP_SECP521R1_ENABLED */
 
-#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA512_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA512,
-#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA512_C */
-
-#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA384_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA384,
-#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA384_C */
-
-#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA256_C)
-    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256,
-#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA256_C */
-
 #if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT) && defined(MBEDTLS_SHA512_C)
     MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512,
 #endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA512_C */
@@ -4379,6 +4367,18 @@ static uint16_t ssl_preset_default_sig_algs[] = {
     MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256,
 #endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT && MBEDTLS_SHA256_C */
 
+#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA512_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA512,
+#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA512_C */
+
+#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA384_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA384,
+#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA384_C */
+
+#if defined(MBEDTLS_RSA_C) &&  defined(MBEDTLS_SHA256_C)
+    MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256,
+#endif /* MBEDTLS_RSA_C && MBEDTLS_SHA256_C */
+
     MBEDTLS_TLS_SIG_NONE
 };
 
diff --git a/library/ssl_tls12_client.c b/library/ssl_tls12_client.c
index 8a109698ce..47557aea9d 100644
--- a/library/ssl_tls12_client.c
+++ b/library/ssl_tls12_client.c
@@ -2041,66 +2041,6 @@ static int ssl_write_encrypted_pms( mbedtls_ssl_context *ssl,
 #endif /* MBEDTLS_KEY_EXCHANGE_RSA_ENABLED ||
           MBEDTLS_KEY_EXCHANGE_RSA_PSK_ENABLED */
 
-#if defined(MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED) ||                       \
-    defined(MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED) ||                     \
-    defined(MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED)
-MBEDTLS_CHECK_RETURN_CRITICAL
-static int ssl_parse_signature_algorithm( mbedtls_ssl_context *ssl,
-                                          unsigned char **p,
-                                          unsigned char *end,
-                                          mbedtls_md_type_t *md_alg,
-                                          mbedtls_pk_type_t *pk_alg )
-{
-    *md_alg = MBEDTLS_MD_NONE;
-    *pk_alg = MBEDTLS_PK_NONE;
-
-    if( (*p) + 2 > end )
-        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
-
-    /*
-     * Get hash algorithm
-     */
-    if( ( *md_alg = mbedtls_ssl_md_alg_from_hash( (*p)[0] ) )
-        == MBEDTLS_MD_NONE )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 1,
-            ( "Server used unsupported HashAlgorithm %d", *(p)[0] ) );
-        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
-    }
-
-    /*
-     * Get signature algorithm
-     */
-    if( ( *pk_alg = mbedtls_ssl_pk_alg_from_sig( (*p)[1] ) )
-        == MBEDTLS_PK_NONE )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 1,
-            ( "server used unsupported SignatureAlgorithm %d", (*p)[1] ) );
-        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
-    }
-
-    /*
-     * Check if the signature algorithm is acceptable
-     */
-    if( !mbedtls_ssl_sig_alg_is_offered( ssl, MBEDTLS_GET_UINT16_BE( *p, 0 ) ) )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 1,
-            ( "server used HashAlgorithm %d that was not offered", *(p)[0] ) );
-        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
-    }
-
-    MBEDTLS_SSL_DEBUG_MSG( 2, ( "Server used SignatureAlgorithm %d",
-                                (*p)[1] ) );
-    MBEDTLS_SSL_DEBUG_MSG( 2, ( "Server used HashAlgorithm %d",
-                                (*p)[0] ) );
-    *p += 2;
-
-    return( 0 );
-}
-#endif /* MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED ||
-          MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED ||
-          MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED */
-
 #if defined(MBEDTLS_KEY_EXCHANGE_ECDH_RSA_ENABLED) || \
     defined(MBEDTLS_KEY_EXCHANGE_ECDH_ECDSA_ENABLED)
 MBEDTLS_CHECK_RETURN_CRITICAL
@@ -2398,14 +2338,31 @@ start_processing:
         unsigned char *params = ssl->in_msg + mbedtls_ssl_hs_hdr_len( ssl );
         size_t params_len = p - params;
         void *rs_ctx = NULL;
+        uint16_t sig_alg;
 
         mbedtls_pk_context * peer_pk;
 
+#if !defined(MBEDTLS_SSL_KEEP_PEER_CERTIFICATE)
+        peer_pk = &ssl->handshake->peer_pubkey;
+#else /* !MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
+        if( ssl->session_negotiate->peer_cert == NULL )
+        {
+            /* Should never happen */
+            MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
+            return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+        }
+        peer_pk = &ssl->session_negotiate->peer_cert->pk;
+#endif /* MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
+
         /*
          * Handle the digitally-signed structure
          */
-        if( ssl_parse_signature_algorithm( ssl, &p, end,
-                                           &md_alg, &pk_alg ) != 0 )
+        MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
+        sig_alg = MBEDTLS_GET_UINT16_BE( p, 0 );
+        if( mbedtls_ssl_tls13_get_pk_type_and_md_alg_from_sig_alg(
+                                            sig_alg, &pk_alg, &md_alg ) != 0 &&
+            ! mbedtls_ssl_sig_alg_is_offered( ssl, sig_alg ) &&
+            ! mbedtls_ssl_sig_alg_is_supported( ssl, sig_alg ) )
         {
             MBEDTLS_SSL_DEBUG_MSG( 1,
                 ( "bad server key exchange message" ) );
@@ -2415,9 +2372,9 @@ start_processing:
                 MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER );
             return( MBEDTLS_ERR_SSL_ILLEGAL_PARAMETER );
         }
+        p += 2;
 
-        if( pk_alg !=
-            mbedtls_ssl_get_ciphersuite_sig_pk_alg( ciphersuite_info ) )
+        if( !mbedtls_pk_can_do( peer_pk, pk_alg ) )
         {
             MBEDTLS_SSL_DEBUG_MSG( 1,
                 ( "bad server key exchange message" ) );
@@ -2475,18 +2432,6 @@ start_processing:
 
         MBEDTLS_SSL_DEBUG_BUF( 3, "parameters hash", hash, hashlen );
 
-#if !defined(MBEDTLS_SSL_KEEP_PEER_CERTIFICATE)
-        peer_pk = &ssl->handshake->peer_pubkey;
-#else /* !MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
-        if( ssl->session_negotiate->peer_cert == NULL )
-        {
-            /* Should never happen */
-            MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
-            return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
-        }
-        peer_pk = &ssl->session_negotiate->peer_cert->pk;
-#endif /* MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
-
         /*
          * Verify signature
          */
@@ -2505,8 +2450,28 @@ start_processing:
             rs_ctx = &ssl->handshake->ecrs_ctx.pk;
 #endif
 
-        if( ( ret = mbedtls_pk_verify_restartable( peer_pk,
-                        md_alg, hash, hashlen, p, sig_len, rs_ctx ) ) != 0 )
+#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
+        if( pk_alg == MBEDTLS_PK_RSASSA_PSS )
+        {
+            const mbedtls_md_info_t* md_info;
+            mbedtls_pk_rsassa_pss_options rsassa_pss_options;
+            rsassa_pss_options.mgf1_hash_id = md_alg;
+            if( ( md_info = mbedtls_md_info_from_type( md_alg ) ) == NULL )
+            {
+                return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+            }
+            rsassa_pss_options.expected_salt_len = mbedtls_md_get_size( md_info );
+            ret = mbedtls_pk_verify_ext( pk_alg, &rsassa_pss_options,
+                                         peer_pk,
+                                         md_alg, hash, hashlen,
+                                         p, sig_len );
+        }
+        else
+#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
+            ret = mbedtls_pk_verify_restartable( peer_pk,
+                        md_alg, hash, hashlen, p, sig_len, rs_ctx );
+
+        if( ret != 0 )
         {
 #if defined(MBEDTLS_SSL_ECP_RESTARTABLE_ENABLED)
             if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )