diff --git a/library/ssl_misc.h b/library/ssl_misc.h
index 6786632..a79869f 100644
--- a/library/ssl_misc.h
+++ b/library/ssl_misc.h
@@ -1980,7 +1980,6 @@
 
     switch( sig_alg )
     {
-#if defined(MBEDTLS_X509_RSASSA_PSS_SUPPORT)
 #if defined(MBEDTLS_SHA256_C)
         case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256:
             *md_alg = MBEDTLS_MD_SHA256;
@@ -1999,7 +1998,6 @@
             *pk_type = MBEDTLS_PK_RSASSA_PSS;
             break;
 #endif /* MBEDTLS_SHA512_C */
-#endif /* MBEDTLS_X509_RSASSA_PSS_SUPPORT */
 
             default:
                 return( MBEDTLS_ERR_SSL_FEATURE_UNAVAILABLE );
@@ -2008,7 +2006,7 @@
 }
 
 #if defined(MBEDTLS_SSL_PROTO_TLS1_3)
-static inline int mbedtls_ssl_tls13_sig_alg_is_supported_for_certificate(
+static inline int mbedtls_ssl_tls13_sig_alg_for_cert_verify_is_supported(
                                                     const uint16_t sig_alg )
 {
     switch( sig_alg )
@@ -2069,7 +2067,7 @@
 #endif /* MBEDTLS_SHA512_C */
 #endif /* MBEDTLS_PKCS1_V15 && MBEDTLS_RSA_C */
         default:
-            return( mbedtls_ssl_tls13_sig_alg_is_supported_for_certificate(
+            return( mbedtls_ssl_tls13_sig_alg_for_cert_verify_is_supported(
                                                                     sig_alg ) );
     }
     return( 1 );
diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index f8e7cc2..2bec6b1 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -4095,13 +4095,12 @@
  *   - ssl_tls12_present* is for TLS 1.2 use only.
  *   - ssl_preset_* is for TLS 1.3 only or hybrid TLS 1.3/1.2 handshakes.
  *
- *   `rsa_pss_rsae_*` MUST BE PUT ARTER `rsa_pkcs1_*` before below compitable fixed
- *   The compitable issue is When
- *   - GnuTLS/OpenSSL is configured as tls12 server with rsa key
- *   - `mebedTLS` is configured as hybrid mode.
- *   - The order is `rsa_pss_rsae_*`, `rsa_pkcs1_*`.
- *   GnuTLS/OpenSSL will return `rsa_pss_rsae_*` which are not supported by
- *   TLS 1.2 in mbedTLS.
+ *   When GnuTLS/Openssl server is configured in TLS 1.2 mode with a certificate
+ *   declaring an RSA public key and Mbed TLS is configured in hybrid mode, if
+ *   `rsa_pss_rsae_*` algorithms are before `rsa_pkcs1_*` ones in this list then
+ *   the  GnuTLS/Openssl server chooses an `rsa_pss_rsae_*` signature algorithm
+ *   for its signature in the key exchange message and as Mbed TLS 1.2 does not
+ *   support them, the handshake fails.
  */
 static uint16_t ssl_preset_default_sig_algs[] = {
 
diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index d470b70..418fc13 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -898,17 +898,17 @@
 #if defined(MBEDTLS_PKCS1_V21)
 #if defined(MBEDTLS_SHA256_C)
                 case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256:
-                    return( key_size <= 2048 );
+                    return( key_size <= 3072 );
 #endif /* MBEDTLS_SHA256_C */
 
 #if defined(MBEDTLS_SHA384_C)
                 case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384:
-                    return( key_size <= 3072 );
+                    return( key_size <= 7680 );
 #endif /* MBEDTLS_SHA384_C */
 
 #if defined(MBEDTLS_SHA512_C)
                 case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512:
-                    return( key_size <= 4096 );
+                    return( 1 );
 #endif /* MBEDTLS_SHA512_C */
 #endif /* MBEDTLS_PKCS1_V21 */
 
@@ -935,7 +935,8 @@
     *algorithm = MBEDTLS_TLS1_3_SIG_NONE;
     for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE ; sig_alg++ )
     {
-        if( mbedtls_ssl_tls13_sig_alg_is_supported_for_certificate( *sig_alg ) &&
+        if( mbedtls_ssl_tls13_sig_alg_for_cert_verify_is_supported(
+                                                            *sig_alg ) &&
             mbedtls_ssl_tls13_check_sig_alg_cert_key_match(
                                                         *sig_alg, own_key ) )
         {