--- a/toolkit/components/startup/tests/browser/browser_bug537449.js
+++ b/toolkit/components/startup/tests/browser/browser_bug537449.js
@@ -1,14 +1,21 @@
 /* This Source Code Form is subject to the terms of the Mozilla Public
  * License, v. 2.0. If a copy of the MPL was not distributed with this
  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
 
 "use strict";
 
+///////////////////
+//
+// Whitelisting this test.
+// As part of bug 1077403, the leaking uncaught rejection should be fixed.
+//
+thisTestLeaksUncaughtRejectionsAndShouldBeFixed("TypeError: this.docShell is null");
+
 const TEST_URL = "http://example.com/browser/toolkit/components/startup/tests/browser/beforeunload.html";
 
 function test() {
   waitForExplicitFinish();
 
   gBrowser.selectedTab = gBrowser.addTab(TEST_URL);
   let browser = gBrowser.selectedBrowser;
 

--- a/toolkit/mozapps/extensions/test/xpinstall/browser_auth3.js
+++ b/toolkit/mozapps/extensions/test/xpinstall/browser_auth3.js
@@ -1,12 +1,21 @@
 // ----------------------------------------------------------------------------
 // Test whether an install fails when authentication is required and it is
 // canceled
 // This verifies bug 312473
+
+///////////////////
+//
+// Whitelisting this test.
+// As part of bug 1077403, the leaking uncaught rejection should be fixed.
+//
+thisTestLeaksUncaughtRejectionsAndShouldBeFixed("TypeError: this.docShell is null");
+
+
 function test() {
   Harness.authenticationCallback = get_auth_info;
   Harness.downloadFailedCallback = download_failed;
   Harness.installEndedCallback = install_ended;
   Harness.installsCompletedCallback = finish_test;
   Harness.setup();
 
   var pm = Services.perms;