diff --git a/includes/form.inc b/includes/form.inc
index 40363d6..c500103 100644
--- a/includes/form.inc
+++ b/includes/form.inc
@@ -4034,6 +4034,21 @@ function element_validate_number($element, &$form_state) {
 }
 
 /**
+ * Filter out a form element's array keys that have empty values.
+ *
+ * This replaces the FAPI hack $form['array_filter'] with the more elegant
+ * $form['item']['#element_validate'] = array('drupal_filter_form_array');
+ *
+ * @param $element
+ *   An associative array containing the structure of the form element.
+ * @param $form_state
+ *   A keyed array containing the current state of the form.
+ */
+function drupal_filter_form_array($element, &$form_state) {
+  $form_state['values'][$element['#name']] = array_keys(array_filter($form_state['values'][$element['#name']]));
+}
+
+/**
  * @} End of "defgroup form_api".
  */
 
diff --git a/modules/book/book.admin.inc b/modules/book/book.admin.inc
index 7b9dea3..5539d2c 100644
--- a/modules/book/book.admin.inc
+++ b/modules/book/book.admin.inc
@@ -37,6 +37,7 @@ function book_admin_settings() {
     '#options' => $types,
     '#description' => t('Users with the %outline-perm permission can add all content types.', array('%outline-perm' => t('Administer book outlines'))),
     '#required' => TRUE,
+    '#element_validate' => array('drupal_filter_form_array'),
   );
   $form['book_child_type'] = array(
     '#type' => 'radios',
@@ -45,7 +46,6 @@ function book_admin_settings() {
     '#options' => $types,
     '#required' => TRUE,
   );
-  $form['array_filter'] = array('#type' => 'value', '#value' => TRUE);
   $form['#validate'][] = 'book_admin_settings_validate';
 
   return system_settings_form($form);
diff --git a/modules/system/system.install b/modules/system/system.install
index 6d80c43..baf5311 100644
--- a/modules/system/system.install
+++ b/modules/system/system.install
@@ -1627,6 +1627,11 @@ function system_update_last_removed() {
  */
 function system_update_8000() {
   // Fill in the first update to Drupal 8 when needed.
+  $ret = array();
+  variable_del('array_filter');
+  $ret[] = array('success' => TRUE, 'query' => "variable_del('array_filter')");
+
+  return $ret;
 }
 
 /**
diff --git a/modules/system/system.module b/modules/system/system.module
index 946ef0c..ea66922 100644
--- a/modules/system/system.module
+++ b/modules/system/system.module
@@ -2759,9 +2759,6 @@ function system_settings_form_submit($form, &$form_state) {
   form_state_values_clean($form_state);
 
   foreach ($form_state['values'] as $key => $value) {
-    if (is_array($value) && isset($form_state['values']['array_filter'])) {
-      $value = array_keys(array_filter($value));
-    }
     variable_set($key, $value);
   }