diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 44a7546..aff2411 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -10066,6 +10066,72 @@
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test    "TLS 1.3: Client authentication, rsa_pss_rsae_sha384 - openssl" \
+            "$O_NEXT_SRV -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache -Verify 10" \
+            "$P_CLI debug_level=4 force_version=tls13 crt_file=data_files/cert_sha256.crt \
+                    key_file=data_files/server1.key sig_algs=ecdsa_secp256r1_sha256,rsa_pss_rsae_sha384" \
+            0 \
+            -c "got a certificate request" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE_VERIFY" \
+            -c "Protocol is TLSv1.3"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_RSA_C
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test    "TLS 1.3: Client authentication, rsa_pss_rsae_sha384 - gnutls" \
+            "$G_NEXT_SRV --debug=4 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:%NO_TICKETS" \
+            "$P_CLI debug_level=3 force_version=tls13 crt_file=data_files/server2-sha256.crt \
+                    key_file=data_files/server2.key sig_algs=ecdsa_secp256r1_sha256,rsa_pss_rsae_sha384" \
+            0 \
+            -c "got a certificate request" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE_VERIFY" \
+            -c "Protocol is TLSv1.3"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_RSA_C
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test    "TLS 1.3: Client authentication, rsa_pss_rsae_sha512 - openssl" \
+            "$O_NEXT_SRV -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache -Verify 10" \
+            "$P_CLI debug_level=4 force_version=tls13 crt_file=data_files/cert_sha256.crt \
+                    key_file=data_files/server1.key sig_algs=ecdsa_secp256r1_sha256,rsa_pss_rsae_sha512" \
+            0 \
+            -c "got a certificate request" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE_VERIFY" \
+            -c "Protocol is TLSv1.3"
+
+requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_RSA_C
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
+run_test    "TLS 1.3: Client authentication, rsa_pss_rsae_sha512 - gnutls" \
+            "$G_NEXT_SRV --debug=4 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:%NO_TICKETS" \
+            "$P_CLI debug_level=3 force_version=tls13 crt_file=data_files/server2-sha256.crt \
+                    key_file=data_files/server2.key sig_algs=ecdsa_secp256r1_sha256,rsa_pss_rsae_sha512" \
+            0 \
+            -c "got a certificate request" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE" \
+            -c "client state: MBEDTLS_SSL_CLIENT_CERTIFICATE_VERIFY" \
+            -c "Protocol is TLSv1.3"
+
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled MBEDTLS_RSA_C
+requires_config_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 run_test    "TLS 1.3: Client authentication, client alg not in server list - openssl" \
             "$O_NEXT_SRV -msg -tls1_3 -num_tickets 0 -no_resume_ephemeral -no_cache -Verify 10
                 -sigalgs ecdsa_secp256r1_sha256" \