diff --git a/lib/dml/tests/mysqli_native_moodle_database_test.php b/lib/dml/tests/mysqli_native_moodle_database_test.php
index dd17338224a..565ee41c266 100644
--- a/lib/dml/tests/mysqli_native_moodle_database_test.php
+++ b/lib/dml/tests/mysqli_native_moodle_database_test.php
@@ -122,7 +122,8 @@ class mysqli_native_moodle_database_test extends \advanced_testcase {
         } catch (moodle_exception $e) {
             // ... or fail.
             // Unfortunately we cannot be sure with the error string.
-            $this->markTestIncomplete('SSL not supported?');
+            $this->markTestSkipped('MySQL server does not support SSL. Unable to complete the test.');
+            return;
         }
 
         try {
diff --git a/lib/dml/tests/pgsql_native_moodle_database_test.php b/lib/dml/tests/pgsql_native_moodle_database_test.php
index 3e0a32e5546..09e6030391d 100644
--- a/lib/dml/tests/pgsql_native_moodle_database_test.php
+++ b/lib/dml/tests/pgsql_native_moodle_database_test.php
@@ -409,7 +409,8 @@ class pgsql_native_moodle_database_test extends \advanced_testcase {
             // ... or fail with SSL not supported.
             $this->assertStringContainsString($pgconnerr, $e->debuginfo);
             $this->assertStringContainsString('server does not support SSL', $e->debuginfo);
-            $this->markTestIncomplete('SSL not supported.');
+            $this->markTestSkipped('Postgres server does not support SSL. Unable to complete the test.');
+            return;
         }
 
         try {