diff --git a/lib/grade/tests/grade_grade_test.php b/lib/grade/tests/grade_grade_test.php
index 29f9a164ba2..fac84ffc3c5 100644
--- a/lib/grade/tests/grade_grade_test.php
+++ b/lib/grade/tests/grade_grade_test.php
@@ -126,11 +126,10 @@ class grade_grade_test extends \grade_base_testcase {
         $this->assertEquals(40, \grade_grade::standardise_score(50, 30, 80, 0, 100));
     }
 
-
-    /*
-     * Disabling this test: the set_locked() arguments have been modified, rendering these tests useless until they are re-written
-
-    protected function test_grade_grade_set_locked() {
+    public function test_grade_grade_set_locked() {
+        // Skip this test because set_locked() arguments have been modified, rendering these tests
+        // useless until they are re-written. Note this comes from MDL-32323 (2012!).
+        $this->markTestSkipped('Useless set_locked() tests until they are re-written');
         $grade_item = new \grade_item($this->grade_items[0]);
         $grade = new \grade_grade($grade_item->get_final(1));
         $this->assertTrue(method_exists($grade, 'set_locked'));
@@ -154,7 +153,6 @@ class grade_grade_test extends \grade_base_testcase {
 
         $this->assertTrue($grade->set_locked(true, false));
     }
-    */
 
     protected function sub_test_grade_grade_is_locked() {
         $grade = new \grade_grade($this->grade_grades[0], false);
diff --git a/lib/phpunit/tests/basic_test.php b/lib/phpunit/tests/basic_test.php
index 88ab7bd6ecb..3950434a8b8 100644
--- a/lib/phpunit/tests/basic_test.php
+++ b/lib/phpunit/tests/basic_test.php
@@ -223,43 +223,50 @@ STRING;
         ];
     }
 
-    // Uncomment following tests to see logging of unexpected changes in global state and database.
-    /*
-        public function test_db_modification() {
-            global $DB;
-            $DB->set_field('user', 'confirmed', 1, array('id'=>-1));
-        }
+    // The following tests are only useful when modifying the reset code and need to check tha
+    // changes in global state are being properly detected. Hence, they are skipped by default.
+    // To run them, remove the markTestSkipped() call when working in that area.
 
-        public function test_cfg_modification() {
-            global $CFG;
-            $CFG->xx = 'yy';
-            unset($CFG->admin);
-            $CFG->rolesactive = 0;
-        }
+    public function test_db_modification() {
+        global $DB;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $DB->set_field('user', 'confirmed', 1, ['id' => -1]);
+    }
 
-        public function test_user_modification() {
-            global $USER;
-            $USER->id = 10;
-        }
+    public function test_cfg_modification() {
+        global $CFG;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $CFG->xx = 'yy';
+        unset($CFG->admin);
+        $CFG->rolesactive = 0;
+    }
 
-        public function test_course_modification() {
-            global $COURSE;
-            $COURSE->id = 10;
-        }
+    public function test_user_modification() {
+        global $USER;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $USER->id = 10;
+    }
 
-        public function test_all_modifications() {
-            global $DB, $CFG, $USER, $COURSE;
-            $DB->set_field('user', 'confirmed', 1, array('id'=>-1));
-            $CFG->xx = 'yy';
-            unset($CFG->admin);
-            $CFG->rolesactive = 0;
-            $USER->id = 10;
-            $COURSE->id = 10;
-        }
+    public function test_course_modification() {
+        global $COURSE;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $COURSE->id = 10;
+    }
 
-        public function test_transaction_problem() {
-            global $DB;
-            $DB->start_delegated_transaction();
-        }
-    */
+    public function test_all_modifications() {
+        global $DB, $CFG, $USER, $COURSE;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $DB->set_field('user', 'confirmed', 1, ['id' => -1]);
+        $CFG->xx = 'yy';
+        unset($CFG->admin);
+        $CFG->rolesactive = 0;
+        $USER->id = 10;
+        $COURSE->id = 10;
+    }
+
+    public function test_transaction_problem() {
+        global $DB;
+        $this->markTestSkipped('This test is only useful to confirm that the reset stuff works as expected.');
+        $DB->start_delegated_transaction();
+    }
 }
diff --git a/lib/tests/rtlcss_test.php b/lib/tests/rtlcss_test.php
index bc6d327755f..80154dbd1b1 100644
--- a/lib/tests/rtlcss_test.php
+++ b/lib/tests/rtlcss_test.php
@@ -1129,12 +1129,11 @@ class rtlcss_test extends basic_testcase {
      * @param array $data the provider data.
      * @dataProvider background_image_provider
      */
-    /* Not supported by MoodleHQ/RTLCSS yet.
     public function test_background_image($data) {
+        $this->markTestSkipped('Not yet supported!');
         $output = new OutputFormat();
         $this->assert_sample($data, $output);
     }
-    */
 
     /**
      * Test background position.
@@ -1197,14 +1196,13 @@ class rtlcss_test extends basic_testcase {
      * @param array $data the provider data.
      * @dataProvider special_provider
      */
-    /* Not supported by MoodleHQ/RTLCSS yet.
     public function test_special($data) {
+        $this->markTestSkipped('Not yet supported!');
         $output = new OutputFormat();
         $output->set('SpaceBeforeRules', ' ');
         $output->set('SpaceAfterListArgumentSeparator', array('default' => '', ',' => ' '));
         $this->assert_sample($data, $output);
     }
-    */
 
     /**
      * Test transform original.
@@ -1226,15 +1224,14 @@ class rtlcss_test extends basic_testcase {
      * @param array $data the provider data.
      * @dataProvider transforms_provider
      */
-    /* Not supported by MoodleHQ/RTLCSS yet.
     public function test_transforms($data) {
+        $this->markTestSkipped('Not yet supported!');
         $output = new OutputFormat();
         $output->set('SpaceBeforeRules', ' ');
         $output->set('SpaceAfterRules', ' ');
         $output->set('SpaceAfterListArgumentSeparator', array('default' => '', ',' => ' '));
         $this->assert_sample($data, $output);
     }
-    */
 
     /**
      * Test values n-syntax.