diff --git a/accessible/tests/mochitest/events/test_docload.html b/accessible/tests/mochitest/events/test_docload.html
index 3d43327a887c..7d3d515430b5 100644
--- a/accessible/tests/mochitest/events/test_docload.html
+++ b/accessible/tests/mochitest/events/test_docload.html
@@ -216,8 +216,11 @@
 
         this.mDialog.close();
 
-        ok(!isAccessibleInCache(dlgDoc),
-           "The document accessible for '" + aURL + "' is in cache still!");
+        // close() is asynchronous.
+        SimpleTest.executeSoon(function() {
+          ok(!isAccessibleInCache(dlgDoc),
+             "The document accessible for '" + aURL + "' is in cache still!");
+        });
       }
 
       this.getID = function openDialogWnd_getID()
diff --git a/accessible/tests/mochitest/relations/test_ui_modalprompt.html b/accessible/tests/mochitest/relations/test_ui_modalprompt.html
index 028456ea5a85..21918b33ce4d 100644
--- a/accessible/tests/mochitest/relations/test_ui_modalprompt.html
+++ b/accessible/tests/mochitest/relations/test_ui_modalprompt.html
@@ -22,12 +22,6 @@
           src="../browser.js"></script>
 
   <script type="application/javascript">
-    if (navigator.platform.startsWith("Mac")) {
-      SimpleTest.expectAssertions(0, 1);
-    } else {
-      SimpleTest.expectAssertions(1);
-    }
-
     function hasTabModalPrompts() {
       try {
         return SpecialPowers.getBoolPref("prompts.tab_modal.enabled");