diff --git a/core/modules/search/lib/Drupal/search/Tests/SearchConfigSettingsFormTest.php b/core/modules/search/lib/Drupal/search/Tests/SearchConfigSettingsFormTest.php
index 4a7186f..ab525dd 100644
--- a/core/modules/search/lib/Drupal/search/Tests/SearchConfigSettingsFormTest.php
+++ b/core/modules/search/lib/Drupal/search/Tests/SearchConfigSettingsFormTest.php
@@ -51,7 +51,7 @@ function setUp() {
     search_update_totals();
 
     // Enable the search block.
-    $this->drupalPlaceBlock('search');
+    $this->drupalPlaceBlock('search_form_block');
   }
 
   /**
diff --git a/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
index d80a76e..713839e 100644
--- a/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
+++ b/core/modules/simpletest/lib/Drupal/simpletest/WebTestBase.php
@@ -377,7 +377,7 @@ protected function drupalCreateContentType($settings = array()) {
   protected function drupalPlaceBlock($plugin_id, array $settings = array(), $theme = NULL) {
     // Confirm that the active user has permission to add the block instance.
     // @todo Remove this check once it is possible to do this programmatically.
-    if (!user_access('administer blocks', $this->loggedInUser)) {
+    if (!empty($this->loggedInUser) && !user_access('administer blocks', $this->loggedInUser)) {
       $this->fail('The logged in user does not have permission to administer blocks.');
       return FALSE;
     }
diff --git a/core/modules/statistics/lib/Drupal/statistics/Tests/StatisticsReportsTest.php b/core/modules/statistics/lib/Drupal/statistics/Tests/StatisticsReportsTest.php
index 1efb7fb..1843c8b 100644
--- a/core/modules/statistics/lib/Drupal/statistics/Tests/StatisticsReportsTest.php
+++ b/core/modules/statistics/lib/Drupal/statistics/Tests/StatisticsReportsTest.php
@@ -88,6 +88,7 @@ function testPopularContentBlock() {
 
     // Configure and save the block.
     $this->drupalPlaceBlock('statistics_popular_block', array(
+      'title' => 'Popular content',
       'statistics_block_top_day_num' => 3,
       'statistics_block_top_all_num' => 3,
       'statistics_block_top_last_num' => 3,
diff --git a/core/modules/system/lib/Drupal/system/Tests/Upgrade/BlockUpgradePathTest.php b/core/modules/system/lib/Drupal/system/Tests/Upgrade/BlockUpgradePathTest.php
index 1ca6e9a..1778284 100644
--- a/core/modules/system/lib/Drupal/system/Tests/Upgrade/BlockUpgradePathTest.php
+++ b/core/modules/system/lib/Drupal/system/Tests/Upgrade/BlockUpgradePathTest.php
@@ -42,9 +42,16 @@ public function testBlockUpgradeTitleLength() {
     $this->drupalGet('');
     $this->assertText($title, 'Block with title longer than 64 characters successfully created.');
 
-    // Add a new custom block with a title over 255 characters.
-    $longer_title = $this->randomName(256);
-    $this->drupalPlaceBlock('system_powered_by_block', array('title' => $longer_title));
+    // Try to add a block with a title over 255 characters.
+    // WebTestBase::drupalPlaceBlock() asserts that the block is created
+    // successfully. In this case we expect the block creation to fail, so
+    // create a new instance of the block manually.
+    $settings = array(
+      'title' => $this->randomName(256),
+      'machine_name' => strtolower($this->randomName(8)),
+      'region' => 'sidebar_first',
+    );
+    $this->drupalPost('admin/structure/block/manage/system_powered_by_block/' . variable_get('theme_default', 'stark'), $settings, t('Save block'));
 
     // Confirm that the custom block cannot be created with title longer than
     // the maximum number of characters.