diff --git a/library/ssl_tls13_server.c b/library/ssl_tls13_server.c
index acb65e38d2..1dde4ab3c9 100644
--- a/library/ssl_tls13_server.c
+++ b/library/ssl_tls13_server.c
@@ -91,7 +91,7 @@ static void ssl_tls13_select_ciphersuite(
         return;
     }
 
-    MBEDTLS_SSL_DEBUG_MSG(2, ("No matched ciphersuite, psk_ciphersuite_id=%x, psk_hash_alg=%lx",
+    MBEDTLS_SSL_DEBUG_MSG(1, ("No matched ciphersuite, psk_ciphersuite_id=%x, psk_hash_alg=%lx",
                               (unsigned) psk_ciphersuite_id,
                               (unsigned long) psk_hash_alg));
 }
diff --git a/tests/suites/test_suite_ssl.function b/tests/suites/test_suite_ssl.function
index 993ae55b41..c365fd674f 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -5046,7 +5046,7 @@ void inject_client_content_on_the_wire(int pk_alg,
     srv_pattern.pattern = log_pattern;
     options.srv_log_obj = &srv_pattern;
     options.srv_log_fun = mbedtls_test_ssl_log_analyzer;
-    mbedtls_debug_set_threshold(5);
+    mbedtls_debug_set_threshold(1);
 
     options.pk_alg = pk_alg;
 
@@ -5078,7 +5078,11 @@ void inject_client_content_on_the_wire(int pk_alg,
         ret = mbedtls_ssl_handshake_step(&server.ssl);
     } while (ret == 0 && server.ssl.state == state);
     TEST_EQUAL(ret,  expected_ret);
-    TEST_EQUAL(srv_pattern.counter, 1);
+    /* If we're expected to suceeed and we do, that's enough.
+     * If we're expected to fail, also check it was in the expected way. */
+    if (expected_ret != 0) {
+        TEST_EQUAL(srv_pattern.counter, 1);
+    }
 
 exit:
     mbedtls_test_free_handshake_options(&options);
@@ -5123,7 +5127,7 @@ void send_large_fragmented_hello(int hs_len_int, int first_frag_content_len_int,
     srv_pattern.pattern = log_pattern;
     options.srv_log_obj = &srv_pattern;
     options.srv_log_fun = mbedtls_test_ssl_log_analyzer;
-    mbedtls_debug_set_threshold(5);
+    mbedtls_debug_set_threshold(1);
 
     // Does't really matter but we want to know to declare dependencies.
     options.pk_alg = MBEDTLS_PK_ECDSA;