diff --git a/core/modules/simpletest/src/TestDiscovery.php b/core/modules/simpletest/src/TestDiscovery.php
index 4c762a7..0366f93 100644
--- a/core/modules/simpletest/src/TestDiscovery.php
+++ b/core/modules/simpletest/src/TestDiscovery.php
@@ -82,6 +82,7 @@ public function registerTestNamespaces() {
 
     // Add PHPUnit test namespaces of Drupal core.
     $this->testNamespaces['Drupal\\Tests\\'] = [DRUPAL_ROOT . '/core/tests/Drupal/Tests'];
+    $this->testNamespaces['Drupal\\KernelTests\\'] = [DRUPAL_ROOT . '/core/tests/Drupal/KernelTests'];
     $this->testNamespaces['Drupal\\FunctionalTests\\'] = [DRUPAL_ROOT . '/core/tests/Drupal/FunctionalTests'];
 
     $this->availableExtensions = array();
@@ -99,6 +100,7 @@ public function registerTestNamespaces() {
 
       // Add PHPUnit test namespaces.
       $this->testNamespaces["Drupal\\Tests\\$name\\Unit\\"][] = "$base_path/tests/src/Unit";
+      $this->testNamespaces["Drupal\\Tests\\$name\\Kernel\\"][] = "$base_path/tests/src/Kernel";
       $this->testNamespaces["Drupal\\Tests\\$name\\Functional\\"][] = "$base_path/tests/src/Functional";
     }
 
diff --git a/core/modules/system/tests/src/Kernel/ModuleHandlerTest.php b/core/modules/system/tests/src/Kernel/Extension/ModuleHandlerTest.php
similarity index 100%
rename from core/modules/system/tests/src/Kernel/ModuleHandlerTest.php
rename to core/modules/system/tests/src/Kernel/Extension/ModuleHandlerTest.php
diff --git a/core/phpunit.xml.dist b/core/phpunit.xml.dist
index e1d3444..15b6316 100644
--- a/core/phpunit.xml.dist
+++ b/core/phpunit.xml.dist
@@ -19,7 +19,6 @@
       <directory>../sites/*/modules/*/tests/src/Unit</directory>
       <!-- Exclude Composer's vendor directory so we don't run tests there. -->
       <exclude>./vendor</exclude>
-      <exclude>./tests/Drupal/Tests/KernelTestBaseTest.php</exclude>
       <!-- Exclude Drush tests. -->
       <exclude>./drush/tests</exclude>
     </testsuite>
diff --git a/core/scripts/run-tests.sh b/core/scripts/run-tests.sh
index 174f14d..79fe45c 100755
--- a/core/scripts/run-tests.sh
+++ b/core/scripts/run-tests.sh
@@ -709,7 +709,7 @@ function simpletest_script_command($test_id, $test_class) {
  * @see simpletest_script_run_one_test()
  */
 function simpletest_script_cleanup($test_id, $test_class, $exitcode) {
-  if (strpos($test_class, 'Drupal\\Tests\\') === 0) {
+  if (is_subclass_of($test_class, '\PHPUnit_Framework_TestCase')) {
     // PHPUnit test, move on.
     return;
   }
diff --git a/core/tests/Drupal/KernelTests/KernelTestBaseTest.php b/core/tests/Drupal/KernelTests/KernelTestBaseTest.php
index f4e351b..6a5c7e7 100644
--- a/core/tests/Drupal/KernelTests/KernelTestBaseTest.php
+++ b/core/tests/Drupal/KernelTests/KernelTestBaseTest.php
@@ -63,7 +63,10 @@ public function testGetDatabaseConnectionInfoWithOutManualSetDbUrl() {
    * @covers ::getDatabaseConnectionInfo
    */
   public function testGetDatabaseConnectionInfoWithManualSetDbUrl() {
-    putenv('SIMPLETEST_DB=sqlite://localhost/:memory:');
+    if (!file_exists('/tmp')) {
+      $this->markTestSkipped();
+    }
+    putenv('SIMPLETEST_DB=sqlite://localhost//tmp/test2.sqlite');
     $this->setUp();
 
     $options = $this->container->get('database')->getConnectionOptions();
diff --git a/core/tests/Drupal/Tests/KernelTestBase.php b/core/tests/Drupal/Tests/KernelTestBase.php
index a5504d0..5736739 100644
--- a/core/tests/Drupal/Tests/KernelTestBase.php
+++ b/core/tests/Drupal/Tests/KernelTestBase.php
@@ -433,7 +433,7 @@ protected function getDatabaseConnectionInfo() {
     // Clone the current connection and replace the current prefix.
     $connection_info = Database::getConnectionInfo('default');
     if (is_null($connection_info)) {
-      throw new \InvalidArgumentException('There is no database connection so no tests can be run. You must provide a SIMPLETEST_DB environment variable to run PHPUnit based functional tests outside of run-tests.sh.');
+      throw new \InvalidArgumentException('There is no database connection so no tests can be run. You must provide a SIMPLETEST_DB environment variable, like "sqlite://localhost//tmp/test.sqlite", to run PHPUnit based functional tests outside of run-tests.sh.');
     }
     else {
       Database::renameConnection('default', 'simpletest_original_default');