diff --git a/core/modules/migrate_drupal/tests/src/Kernel/StateFileExists.php b/core/modules/migrate_drupal/tests/src/Kernel/StateFileExists.php
index 240fd8fb46..102c5bc564 100644
--- a/core/modules/migrate_drupal/tests/src/Kernel/StateFileExists.php
+++ b/core/modules/migrate_drupal/tests/src/Kernel/StateFileExists.php
@@ -70,6 +70,7 @@ class StateFileExists extends MigrateDrupalTestBase {
     'rdf',
     'search',
     'shortcut',
+    'simpletest',
     'statistics',
     'syslog',
     'system',
diff --git a/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php b/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
index 3c87b9acbd..1e1b2fc579 100644
--- a/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
+++ b/core/modules/system/tests/src/Functional/Form/ModulesListFormWebTest.php
@@ -45,11 +45,10 @@ public function testModuleListForm() {
     // Check that system_test's help link was rendered correctly.
     $this->assertFieldByXPath("//a[contains(@href, '/admin/help/system_test') and @title='Help']");
 
-    $this->markTestIncomplete('We need to figure out how to test that the module form is displaying both display and machine name.');
     // Ensure that the Testing module's machine name is printed. Testing module
     // is used because its machine name is different than its human readable
     // name.
-    // $this->assertText('simpletest');
+    $this->assertText('simpletest');
   }
 
   public function testModulesListFormWithInvalidInfoFile() {
diff --git a/core/tests/Drupal/KernelTests/Core/Asset/AttachedAssetsTest.php b/core/tests/Drupal/KernelTests/Core/Asset/AttachedAssetsTest.php
index 1523f6f9f9..520063c0ef 100644
--- a/core/tests/Drupal/KernelTests/Core/Asset/AttachedAssetsTest.php
+++ b/core/tests/Drupal/KernelTests/Core/Asset/AttachedAssetsTest.php
@@ -38,7 +38,7 @@ class AttachedAssetsTest extends KernelTestBase {
   /**
    * {@inheritdoc}
    */
-  public static $modules = ['language', 'common_test', 'system'];
+  public static $modules = ['language', 'simpletest', 'common_test', 'system'];
 
   /**
    * {@inheritdoc}
@@ -387,7 +387,6 @@ public function testRenderDifferentWeight() {
    * @see simpletest_js_alter()
    */
   public function testAlter() {
-    $this->markTestIncomplete('Determine whether we actually need to test the simpletest JS.');
     // Add both tableselect.js and simpletest.js.
     $build['#attached']['library'][] = 'core/drupal.tableselect';
     $build['#attached']['library'][] = 'simpletest/drupal.simpletest';