diff --git a/browsertest-convert.php b/browsertest-convert.php
index 65c0dbe..a2c3dfb 100644
--- a/browsertest-convert.php
+++ b/browsertest-convert.php
@@ -121,6 +121,7 @@
   'NodeViewTest',
   'ShortcutLinksTest',
   'TermTest',
+  'TermAutocompleteTest',
   'UserAccountLinksTest',
 
   // @todo ... there are more
@@ -555,7 +556,7 @@ function glob_recursive($pattern, $flags = 0) {
       continue;
     }
     // REST tests are not converted yet.
-    if (strpos($file_content, ' extends RestTestBase {') !== FALSE) {
+    if (strpos($file_content, ' extends RESTTestBase {') !== FALSE) {
       continue;
     }
     // Module tests should be refactored into kernel and browser tests.
@@ -598,6 +599,12 @@ function glob_recursive($pattern, $flags = 0) {
     // Fix use statements for base classes.
     str_replace("use Drupal\\system\\Tests\\Cache\\PageCacheTagsTestBase;", "use Drupal\\Tests\\system\\Functional\\Cache\\PageCacheTagsTestBase;", $file_content);
 
+    // Use AssertMailTrait where needed.
+    if (strpos($file_content, '$this->drupalGetMails(') !== FALSE) {
+      $file_content = str_replace(" extends BrowserTestBase {", " extends BrowserTestBase {\n  use AssertMailTrait {\n    getMails as drupalGetMails;\n  }", $file_content);
+      $file_content = str_replace("use Drupal\\Tests\\BrowserTestBase;", "use Drupal\\Tests\\BrowserTestBase;\nuse Drupal\Core\Test\AssertMailTrait;", $file_content);
+    }
+
     $test_dir = dirname("$browsertest_dir/$file_name");
     if (!file_exists($test_dir)) {
       mkdir($test_dir, 0777, TRUE);
diff --git a/core/modules/dblog/tests/src/Functional/Rest/DbLogResourceTest.php b/core/modules/dblog/src/Tests/Rest/DbLogResourceTest.php
similarity index 98%
rename from core/modules/dblog/tests/src/Functional/Rest/DbLogResourceTest.php
rename to core/modules/dblog/src/Tests/Rest/DbLogResourceTest.php
index ad75e63..279d202 100644
--- a/core/modules/dblog/tests/src/Functional/Rest/DbLogResourceTest.php
+++ b/core/modules/dblog/src/Tests/Rest/DbLogResourceTest.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\Tests\dblog\Functional\Rest;
+namespace Drupal\dblog\Tests\Rest;
 
 use Drupal\Component\Serialization\Json;
 use Drupal\Core\Url;
diff --git a/core/modules/simpletest/tests/src/Functional/MailCaptureTest.php b/core/modules/simpletest/tests/src/Functional/MailCaptureTest.php
index 1c0c533..b79db8d 100644
--- a/core/modules/simpletest/tests/src/Functional/MailCaptureTest.php
+++ b/core/modules/simpletest/tests/src/Functional/MailCaptureTest.php
@@ -3,6 +3,7 @@
 namespace Drupal\Tests\simpletest\Functional;
 
 use Drupal\Tests\BrowserTestBase;
+use Drupal\Core\Test\AssertMailTrait;
 
 /**
  * Tests the SimpleTest email capturing logic, the assertMail assertion and the
@@ -11,6 +12,9 @@
  * @group simpletest
  */
 class MailCaptureTest extends BrowserTestBase {
+  use AssertMailTrait {
+    getMails as drupalGetMails;
+  }
   /**
    * Test to see if the wrapper function is executed correctly.
    */
diff --git a/core/modules/system/tests/src/Functional/System/ResponseGeneratorTest.php b/core/modules/system/src/Tests/System/ResponseGeneratorTest.php
similarity index 97%
rename from core/modules/system/tests/src/Functional/System/ResponseGeneratorTest.php
rename to core/modules/system/src/Tests/System/ResponseGeneratorTest.php
index d4717b1..f54c651 100644
--- a/core/modules/system/tests/src/Functional/System/ResponseGeneratorTest.php
+++ b/core/modules/system/src/Tests/System/ResponseGeneratorTest.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\Tests\system\Functional\System;
+namespace Drupal\system\Tests\System;
 
 use Drupal\rest\Tests\RESTTestBase;
 
diff --git a/core/modules/system/tests/src/Functional/Path/UrlAlterFunctionalTest.php b/core/modules/system/tests/src/Functional/Path/UrlAlterFunctionalTest.php
index baa4d30..a24ddf9 100644
--- a/core/modules/system/tests/src/Functional/Path/UrlAlterFunctionalTest.php
+++ b/core/modules/system/tests/src/Functional/Path/UrlAlterFunctionalTest.php
@@ -3,8 +3,8 @@
 namespace Drupal\Tests\system\Functional\Path;
 
 use Drupal\Core\Database\Database;
-use Drupal\Tests\BrowserTestBase;
 use Drupal\Core\Url;
+use Drupal\Tests\BrowserTestBase;
 use Drupal\taxonomy\Entity\Term;
 
 /**
diff --git a/core/modules/user/tests/src/Functional/RestRegisterUserTest.php b/core/modules/user/src/Tests/RestRegisterUserTest.php
similarity index 99%
rename from core/modules/user/tests/src/Functional/RestRegisterUserTest.php
rename to core/modules/user/src/Tests/RestRegisterUserTest.php
index 576bd3e..62e6bbc 100644
--- a/core/modules/user/tests/src/Functional/RestRegisterUserTest.php
+++ b/core/modules/user/src/Tests/RestRegisterUserTest.php
@@ -1,6 +1,6 @@
 <?php
 
-namespace Drupal\Tests\user\Functional;
+namespace Drupal\user\Tests;
 
 use Drupal\rest\Tests\RESTTestBase;
 use Drupal\user\Entity\Role;
diff --git a/core/tests/Drupal/Tests/BrowserTestBase.php b/core/tests/Drupal/Tests/BrowserTestBase.php
index f135748..ba08cd5 100644
--- a/core/tests/Drupal/Tests/BrowserTestBase.php
+++ b/core/tests/Drupal/Tests/BrowserTestBase.php
@@ -22,7 +22,6 @@
 use Drupal\Core\Session\UserSession;
 use Drupal\Core\Site\Settings;
 use Drupal\Core\StreamWrapper\StreamWrapperInterface;
-use Drupal\Core\Test\AssertMailTrait;
 use Drupal\Core\Test\TestRunnerKernel;
 use Drupal\Core\Url;
 use Drupal\Core\Utility\Error;
@@ -68,9 +67,6 @@
     createUser as drupalCreateUser;
   }
   use XdebugRequestTrait;
-  use AssertMailTrait {
-    getMails as drupalGetMails;
-  }
 
   /**
    * Class loader.