diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index 54884e9..858fe03 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -923,83 +923,13 @@
     return( 0 );
 }
 
-#if defined(MBEDTLS_USE_PSA_CRYPTO)
-static psa_algorithm_t ssl_tls13_select_sig_alg_to_psa_alg( uint16_t sig_alg )
-{
-    switch( sig_alg )
-    {
-        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP256R1_SHA256:
-            return( PSA_ALG_ECDSA( PSA_ALG_SHA_256 ) );
-        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP384R1_SHA384:
-            return( PSA_ALG_ECDSA( PSA_ALG_SHA_384 ) );
-        case MBEDTLS_TLS1_3_SIG_ECDSA_SECP521R1_SHA512:
-            return( PSA_ALG_ECDSA( PSA_ALG_SHA_512 ) );
-        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256:
-            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_256 ) );
-        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384:
-            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_384 ) );
-        case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512:
-            return( PSA_ALG_RSA_PSS( PSA_ALG_SHA_512 ) );
-        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256:
-        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA384:
-        case MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA512:
-            return( PSA_ALG_RSA_PKCS1V15_CRYPT );
-        default:
-            return( 0 );
-    }
-}
-#endif /* MBEDTLS_USE_PSA_CRYPTO */
-
-MBEDTLS_CHECK_RETURN_CRITICAL
-static int ssl_tls13_select_sig_alg_for_certificate_verify(
-                                          mbedtls_ssl_context *ssl,
-                                          mbedtls_pk_context *own_key,
-                                          uint16_t *algorithm )
-{
-    uint16_t *sig_alg = ssl->handshake->received_sig_algs;
-#if defined(MBEDTLS_USE_PSA_CRYPTO)
-    psa_algorithm_t psa_alg = 0;
-#endif /* MBEDTLS_USE_PSA_CRYPTO */
-
-    *algorithm = MBEDTLS_TLS1_3_SIG_NONE;
-    for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE ; sig_alg++ )
-    {
-#if defined(MBEDTLS_USE_PSA_CRYPTO)
-        psa_alg = ssl_tls13_select_sig_alg_to_psa_alg( *sig_alg );
-#endif /* MBEDTLS_USE_PSA_CRYPTO */
-
-        if( mbedtls_ssl_sig_alg_is_offered( ssl, *sig_alg ) &&
-            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 )
-#if defined(MBEDTLS_USE_PSA_CRYPTO)
-            && psa_alg != 0 &&
-            mbedtls_pk_can_do_ext( own_key, psa_alg,
-                                   PSA_KEY_USAGE_SIGN_HASH ) == 1
-#endif /* MBEDTLS_USE_PSA_CRYPTO */
-            )
-        {
-            MBEDTLS_SSL_DEBUG_MSG( 3,
-                                   ( "select_sig_alg_for_certificate_verify:"
-                                     "selected signature algorithm %s [%04x]",
-                                     mbedtls_ssl_sig_alg_to_str( *sig_alg ),
-                                     *sig_alg ) );
-            *algorithm = *sig_alg;
-            return( 0 );
-        }
-    }
-    MBEDTLS_SSL_DEBUG_MSG( 2,
-                           ( "select_sig_alg_for_certificate_verify:"
-                             "no suitable signature algorithm found" ) );
-    return( -1 );
-}
-
 MBEDTLS_CHECK_RETURN_CRITICAL
 static int ssl_tls13_write_certificate_verify_body( mbedtls_ssl_context *ssl,
                                                     unsigned char *buf,
                                                     unsigned char *end,
                                                     size_t *out_len )
 {
-    int ret;
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
     unsigned char *p = buf;
     mbedtls_pk_context *own_key;
 
@@ -1007,14 +937,9 @@
     size_t handshake_hash_len;
     unsigned char verify_buffer[ SSL_VERIFY_STRUCT_MAX_SIZE ];
     size_t verify_buffer_len;
-    mbedtls_pk_type_t pk_type = MBEDTLS_PK_NONE;
-    mbedtls_md_type_t md_alg = MBEDTLS_MD_NONE;
-    psa_algorithm_t psa_algorithm = PSA_ALG_NONE;
-    uint16_t algorithm = MBEDTLS_TLS1_3_SIG_NONE;
+
+    uint16_t *sig_alg = ssl->handshake->received_sig_algs;
     size_t signature_len = 0;
-    unsigned char verify_hash[PSA_HASH_MAX_SIZE];
-    size_t verify_hash_len;
-    psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
 
     *out_len = 0;
 
@@ -1047,64 +972,78 @@
      *    opaque signature<0..2^16-1>;
      *  } CertificateVerify;
      */
-    ret = ssl_tls13_select_sig_alg_for_certificate_verify( ssl, own_key,
-                                                           &algorithm );
-    if( ret != 0 )
+    /* Check there is space for the algorithm identifier (2 bytes) and the
+     * signature length (2 bytes).
+     */
+    MBEDTLS_SSL_CHK_BUF_PTR( p, end, 4 );
+
+    for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE ; sig_alg++ )
     {
-        MBEDTLS_SSL_DEBUG_MSG( 1,
-                    ( "signature algorithm not in received or offered list." ) );
+        psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
+        mbedtls_pk_type_t pk_type = MBEDTLS_PK_NONE;
+        mbedtls_md_type_t md_alg = MBEDTLS_MD_NONE;
+        psa_algorithm_t psa_algorithm = PSA_ALG_NONE;
+        unsigned char verify_hash[PSA_HASH_MAX_SIZE];
+        size_t verify_hash_len;
 
-        MBEDTLS_SSL_DEBUG_MSG( 1, ( "Signature algorithm is %s",
-                                    mbedtls_ssl_sig_alg_to_str( algorithm ) ) );
+        if( !mbedtls_ssl_sig_alg_is_offered( ssl, *sig_alg ) )
+            continue;
 
+        if( !mbedtls_ssl_tls13_sig_alg_for_cert_verify_is_supported( *sig_alg ) )
+            continue;
+
+        if( !mbedtls_ssl_tls13_check_sig_alg_cert_key_match( *sig_alg, own_key ) )
+            continue;
+
+        if( mbedtls_ssl_get_pk_type_and_md_alg_from_sig_alg(
+                                        *sig_alg, &pk_type, &md_alg ) != 0 )
+        {
+             return( MBEDTLS_ERR_SSL_INTERNAL_ERROR  );
+        }
+
+        /* Hash verify buffer with indicated hash function */
+        psa_algorithm = mbedtls_hash_info_psa_from_md( md_alg );
+        status = psa_hash_compute( psa_algorithm,
+                                   verify_buffer,
+                                   verify_buffer_len,
+                                   verify_hash, sizeof( verify_hash ),
+                                   &verify_hash_len );
+        if( status != PSA_SUCCESS )
+            return( psa_ssl_status_to_mbedtls( status ) );
+
+        MBEDTLS_SSL_DEBUG_BUF( 3, "verify hash", verify_hash, verify_hash_len );
+
+        if( ( ret = mbedtls_pk_sign_ext( pk_type, own_key,
+                        md_alg, verify_hash, verify_hash_len,
+                        p + 4, (size_t)( end - ( p + 4 ) ), &signature_len,
+                        ssl->conf->f_rng, ssl->conf->p_rng ) ) != 0 )
+        {
+             MBEDTLS_SSL_DEBUG_MSG( 2, ( "CertificateVerify signature failed with %s",
+                                    mbedtls_ssl_sig_alg_to_str( *sig_alg ) ) );
+             MBEDTLS_SSL_DEBUG_RET( 2, "mbedtls_pk_sign_ext", ret );
+             continue;
+        }
+
+        MBEDTLS_SSL_DEBUG_MSG( 2, ( "CertificateVerify signature with %s",
+                                    mbedtls_ssl_sig_alg_to_str( *sig_alg ) ) );
+
+        break;
+    }
+
+    if( *sig_alg == MBEDTLS_TLS1_3_SIG_NONE )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1, ( "no suitable signature algorithm" ) );
         MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_HANDSHAKE_FAILURE,
                                       MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
         return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
     }
 
-    MBEDTLS_SSL_DEBUG_MSG( 2, ( "CertificateVerify with %s",
-                                mbedtls_ssl_sig_alg_to_str( algorithm )) );
+    MBEDTLS_PUT_UINT16_BE( *sig_alg, p, 0 );
+    MBEDTLS_PUT_UINT16_BE( signature_len, p, 2 );
 
-    if( mbedtls_ssl_get_pk_type_and_md_alg_from_sig_alg(
-                                        algorithm, &pk_type, &md_alg ) != 0 )
-    {
-        return( MBEDTLS_ERR_SSL_INTERNAL_ERROR  );
-    }
+    *out_len = 4 + signature_len;
 
-    /* Check there is space for the algorithm identifier (2 bytes) and the
-     * signature length (2 bytes).
-     */
-    MBEDTLS_SSL_CHK_BUF_PTR( p, end, 4 );
-    MBEDTLS_PUT_UINT16_BE( algorithm, p, 0 );
-    p += 2;
-
-    /* Hash verify buffer with indicated hash function */
-    psa_algorithm = mbedtls_hash_info_psa_from_md( md_alg );
-    status = psa_hash_compute( psa_algorithm,
-                               verify_buffer,
-                               verify_buffer_len,
-                               verify_hash,sizeof( verify_hash ),
-                               &verify_hash_len );
-    if( status != PSA_SUCCESS )
-        return( psa_ssl_status_to_mbedtls( status ) );
-
-    MBEDTLS_SSL_DEBUG_BUF( 3, "verify hash", verify_hash, verify_hash_len );
-
-    if( ( ret = mbedtls_pk_sign_ext( pk_type, own_key,
-                        md_alg, verify_hash, verify_hash_len,
-                        p + 2, (size_t)( end - ( p + 2 ) ), &signature_len,
-                        ssl->conf->f_rng, ssl->conf->p_rng ) ) != 0 )
-    {
-        MBEDTLS_SSL_DEBUG_RET( 1, "mbedtls_pk_sign", ret );
-        return( ret );
-    }
-
-    MBEDTLS_PUT_UINT16_BE( signature_len, p, 0 );
-    p += 2 + signature_len;
-
-    *out_len = (size_t)( p - buf );
-
-    return( ret );
+    return( 0 );
 }
 
 int mbedtls_ssl_tls13_write_certificate_verify( mbedtls_ssl_context *ssl )