diff --git a/admin/settings/server.php b/admin/settings/server.php
index 85e3f2dc6c3..3a58d34479e 100644
--- a/admin/settings/server.php
+++ b/admin/settings/server.php
@@ -175,16 +175,25 @@ $ADMIN->add('server', new admin_externalpage('phpinfo', new lang_string('phpinfo
 // "performance" settingpage
 $temp = new admin_settingpage('performance', new lang_string('performance', 'admin'));
 
+// Memory limit options for large administration tasks.
+$memoryoptions = array(
+    '64M' => '64M',
+    '128M' => '128M',
+    '256M' => '256M',
+    '512M' => '512M',
+    '1024M' => '1024M',
+    '2048M' => '2048M');
+
+// Allow larger memory usage for 64-bit sites only.
+if (PHP_INT_SIZE === 8) {
+    $memoryoptions['3072M'] = '3072M';
+    $memoryoptions['4096M'] = '4096M';
+}
+
 $temp->add(new admin_setting_configselect('extramemorylimit', new lang_string('extramemorylimit', 'admin'),
                                           new lang_string('configextramemorylimit', 'admin'), '512M',
-                                          // if this option is set to 0, default 128M will be used
-                                          array( '64M' => '64M',
-                                                 '128M' => '128M',
-                                                 '256M' => '256M',
-                                                 '512M' => '512M',
-                                                 '1024M' => '1024M',
-                                                 '2048M' => '2048M',
-                                             )));
+                                          $memoryoptions));
+
 $temp->add(new admin_setting_configtext('curlcache', new lang_string('curlcache', 'admin'),
                                         new lang_string('configcurlcache', 'admin'), 120, PARAM_INT));
 
diff --git a/backup/backup.php b/backup/backup.php
index 2847665f4fa..cfe16efb364 100644
--- a/backup/backup.php
+++ b/backup/backup.php
@@ -79,6 +79,10 @@ switch ($type) {
         print_error('unknownbackuptype');
 }
 
+// Backup of large courses requires extra memory. Use the amount configured
+// in admin settings.
+raise_memory_limit(MEMORY_EXTRA);
+
 if (!($bc = backup_ui::load_controller($backupid))) {
     $bc = new backup_controller($type, $id, backup::FORMAT_MOODLE,
                             backup::INTERACTIVE_YES, backup::MODE_GENERAL, $USER->id);
diff --git a/backup/restore.php b/backup/restore.php
index 6091c092bbc..cd51caebdeb 100644
--- a/backup/restore.php
+++ b/backup/restore.php
@@ -17,6 +17,10 @@ $PAGE->set_pagelayout('standard');
 require_login($course, null, $cm);
 require_capability('moodle/restore:restorecourse', $context);
 
+// Restore of large courses requires extra memory. Use the amount configured
+// in admin settings.
+raise_memory_limit(MEMORY_EXTRA);
+
 if ($stage & restore_ui::STAGE_CONFIRM + restore_ui::STAGE_DESTINATION) {
     $restore = restore_ui::engage_independent_stage($stage, $contextid);
 } else {
diff --git a/lib/setuplib.php b/lib/setuplib.php
index a74a1d34c45..2de85e5b0a5 100644
--- a/lib/setuplib.php
+++ b/lib/setuplib.php
@@ -1026,7 +1026,14 @@ function raise_memory_limit($newlimit) {
         }
 
     } else if ($newlimit == MEMORY_HUGE) {
+        // MEMORY_HUGE uses 2G or MEMORY_EXTRA, whichever is bigger.
         $newlimit = get_real_size('2G');
+        if (!empty($CFG->extramemorylimit)) {
+            $extra = get_real_size($CFG->extramemorylimit);
+            if ($extra > $newlimit) {
+                $newlimit = $extra;
+            }
+        }
 
     } else {
         $newlimit = get_real_size($newlimit);