diff --git a/composer.json b/composer.json
index c3aa4f3509..3bfb0c7779 100644
--- a/composer.json
+++ b/composer.json
@@ -53,7 +53,7 @@
         "post-package-install": "Drupal\\Core\\Composer\\Composer::vendorTestCodeCleanup",
         "post-package-update": "Drupal\\Core\\Composer\\Composer::vendorTestCodeCleanup",
         "post-install-cmd": "Drupal\\Core\\Composer\\Composer::upgradePHPUnit",
-        "drupal-phpunit-upgrade": "@composer upgrade phpunit/phpunit --with-dependencies --no-progress",
+        "drupal-phpunit-upgrade": "@composer update phpunit/phpunit --with-dependencies --no-progress",
         "phpcs": "phpcs --standard=core/phpcs.xml.dist --runtime-set installed_paths $($COMPOSER_BINARY config vendor-dir)/drupal/coder/coder_sniffer --",
         "phpcbf": "phpcbf --standard=core/phpcs.xml.dist --runtime-set installed_paths $($COMPOSER_BINARY config vendor-dir)/drupal/coder/coder_sniffer --"
     },
diff --git a/core/composer.json b/core/composer.json
index c4bb384b92..797a9f9e37 100644
--- a/core/composer.json
+++ b/core/composer.json
@@ -44,7 +44,7 @@
         "jcalderonzumba/gastonjs": "^1.0.2",
         "jcalderonzumba/mink-phantomjs-driver": "^0.3.1",
         "mikey179/vfsStream": "^1.2",
-        "phpunit/phpunit": "^4.8.35 || ^6.1",
+        "phpunit/phpunit": "^4.8.35 || ^6.0",
         "phpspec/prophecy": "^1.4",
         "symfony/css-selector": "~3.2.8",
         "symfony/phpunit-bridge": "^3.4.0@beta"
diff --git a/core/lib/Drupal/Core/Composer/Composer.php b/core/lib/Drupal/Core/Composer/Composer.php
index 0c96b9b20f..9d3d386596 100644
--- a/core/lib/Drupal/Core/Composer/Composer.php
+++ b/core/lib/Drupal/Core/Composer/Composer.php
@@ -160,9 +160,9 @@ public static function upgradePHPUnit(Event $event) {
       return;
     }
 
-    // If the PHP version is 7.1 or above and PHPUnit is less than version 6
+    // If the PHP version is 7.2 or above and PHPUnit is less than version 6
     // call the drupal-phpunit-upgrade script to upgrade PHPUnit.
-    if (version_compare(PHP_MAJOR_VERSION . '.' . PHP_MINOR_VERSION, '7.1') >= 0 && version_compare($phpunit_package->getVersion(), '6.0') < 0) {
+    if (version_compare(PHP_MAJOR_VERSION . '.' . PHP_MINOR_VERSION, '7.2') >= 0 && version_compare($phpunit_package->getVersion(), '6.0') < 0) {
       $event->getComposer()
         ->getEventDispatcher()
         ->dispatchScript('drupal-phpunit-upgrade');
diff --git a/core/modules/tour/src/Tests/TourTestBase.php b/core/modules/tour/src/Tests/TourTestBase.php
index f551c8151b..e139650706 100644
--- a/core/modules/tour/src/Tests/TourTestBase.php
+++ b/core/modules/tour/src/Tests/TourTestBase.php
@@ -14,17 +14,6 @@
  */
 abstract class TourTestBase extends WebTestBase {
 
-  /**
-   * {@inheritdoc}
-   */
-  protected function setUp() {
-    // Support both PHPUnit 4 and 6.
-    if (!class_exists('\PHPUnit_Util_XML') && class_exists('\PHPUnit\Util\XML')) {
-      class_alias('\PHPUnit\Util\XML', '\PHPUnit_Util_XML');
-    }
-    parent::setUp();
-  }
-
   /**
    * Assert function to determine if tips rendered to the page
    * have a corresponding page element.
diff --git a/core/scripts/run-tests.sh b/core/scripts/run-tests.sh
index e545318b87..407d87a34f 100755
--- a/core/scripts/run-tests.sh
+++ b/core/scripts/run-tests.sh
@@ -794,9 +794,9 @@ function simpletest_script_run_one_test($test_id, $test_class) {
     }
     else {
       // Prevent deprecations caused by vendor code calling deprecated code.
-      // This also prevents PHPUnit 6's mock code that triggers silenced
+      // This also prevents mock objects in PHPUnit 6 triggering silenced
       // deprecations from breaking the test suite. We should consider changing
-      // this to 'strict' once we are no longer use PHPUnit 4.
+      // this to 'strict' once PHPUnit 4 is no longer used.
       putenv('SYMFONY_DEPRECATIONS_HELPER=weak_vendors');
     }
     if (is_subclass_of($test_class, TestCase::class)) {
diff --git a/core/tests/Drupal/KernelTests/Core/Messenger/LegacyMessengerTest.php b/core/tests/Drupal/KernelTests/Core/Messenger/MessengerTest.php
similarity index 98%
rename from core/tests/Drupal/KernelTests/Core/Messenger/LegacyMessengerTest.php
rename to core/tests/Drupal/KernelTests/Core/Messenger/MessengerTest.php
index 13f10e9c2e..362069756e 100644
--- a/core/tests/Drupal/KernelTests/Core/Messenger/LegacyMessengerTest.php
+++ b/core/tests/Drupal/KernelTests/Core/Messenger/MessengerTest.php
@@ -11,7 +11,7 @@
  * @group Messenger
  * @coversDefaultClass \Drupal\Core\Messenger\LegacyMessenger
  */
-class LegacyMessengerTest extends KernelTestBase {
+class MessengerTest extends KernelTestBase {
 
   /**
    * Retrieves the Messenger service from LegacyMessenger.