diff --git a/modules/simpletest/tests/common.test b/modules/simpletest/tests/common.test
index 7e79450..5650d8c 100644
--- a/modules/simpletest/tests/common.test
+++ b/modules/simpletest/tests/common.test
@@ -524,7 +524,7 @@ class CommonSizeTestCase extends DrupalUnitTestCase {
 /**
  * Test drupal_explode_tags() and drupal_implode_tags().
  */
-class DrupalTagsHandlingTestCase extends DrupalWebTestCase {
+class DrupalTagsHandlingTestCase extends DrupalUnitTestCase {
   var $validTags = array(
     'Drupal' => 'Drupal',
     'Drupal with some spaces' => 'Drupal with some spaces',
@@ -2113,7 +2113,7 @@ class DrupalErrorCollectionUnitTest extends DrupalWebTestCase {
 /**
  * Test the drupal_parse_info_file() API function.
  */
-class ParseInfoFilesTestCase extends DrupalWebTestCase {
+class ParseInfoFilesTestCase extends DrupalUnitTestCase {
   public static function getInfo() {
     return array(
       'name' => 'Parsing .info files',
diff --git a/modules/simpletest/tests/unicode.test b/modules/simpletest/tests/unicode.test
index 47a4938..cf7991b 100644
--- a/modules/simpletest/tests/unicode.test
+++ b/modules/simpletest/tests/unicode.test
@@ -8,7 +8,7 @@
 /**
  * Test unicode handling features implemented in unicode.inc.
  */
-class UnicodeUnitTest extends DrupalWebTestCase {
+class UnicodeUnitTest extends DrupalUnitTestCase {
 
   /**
    * Whether to run the extended version of the tests (including non latin1 characters).