diff --git a/toolkit/components/places/tests/head_common.js b/toolkit/components/places/tests/head_common.js
index 8e5a5866e203..87707ba2c248 100644
--- a/toolkit/components/places/tests/head_common.js
+++ b/toolkit/components/places/tests/head_common.js
@@ -508,3 +508,21 @@ let (randomFailingSyncTests = [
     sync.observe(null, "places-debug-stop-sync", null);
   }
 }
+
+// These tests are randomly failing if idle-daily is executed in the middle,
+// thus we make history ignore the notification for them.  See bug 602872.
+let (randomFailingIdleTests = [
+  "test_redirectsMode.js",
+  "test_tags.js",
+  "test_history_sidebar.js",
+  "test_removeVisitsByTimeframe.js",
+  "test_history_removeAllPages.js", // Needs stable frecency.
+  "test_database_sync_after_shutdown_with_removeAllPages.js", // Needs stable frecency.
+]) {
+  let currentTestFilename = do_get_file(_TEST_FILE[0], true).leafName;
+  if (randomFailingIdleTests.indexOf(currentTestFilename) != -1) {
+    print("Test " + currentTestFilename +
+          " is known random due to idle-daily, remove observer.");
+    Services.obs.removeObserver(PlacesUtils.history, "idle-daily");
+  }
+}
diff --git a/toolkit/components/places/tests/sync/test_database_sync_after_shutdown_with_removeAllPages.js b/toolkit/components/places/tests/sync/test_database_sync_after_shutdown_with_removeAllPages.js
index af75b9b2a669..4c68a2325dbb 100644
--- a/toolkit/components/places/tests/sync/test_database_sync_after_shutdown_with_removeAllPages.js
+++ b/toolkit/components/places/tests/sync/test_database_sync_after_shutdown_with_removeAllPages.js
@@ -138,10 +138,6 @@ function run_test()
 {
   do_test_pending();
 
-  // Since we are checking frecency, we have to disable some stuff that could
-  // change values during test run.  On idle-daily frecencies are updated.
-  Services.obs.removeObserver(PlacesUtils.history, "idle-daily");
-
   // Set the preference for the timer to a really large value, so it won't
   // run before the test finishes.
   prefs.setIntPref(PREF_SYNC_INTERVAL, SYNC_INTERVAL);
diff --git a/toolkit/components/places/tests/unit/test_history_removeAllPages.js b/toolkit/components/places/tests/unit/test_history_removeAllPages.js
index 238ec90f511a..48aa75a8138b 100644
--- a/toolkit/components/places/tests/unit/test_history_removeAllPages.js
+++ b/toolkit/components/places/tests/unit/test_history_removeAllPages.js
@@ -237,10 +237,6 @@ os.addObserver(syncObserver, kSyncFinished, false);
 
 // main
 function run_test() {
-  // Since we are checking frecency, we have to disable some stuff that could
-  // change values during test run.  On idle-daily frecencies are updated.
-  Services.obs.removeObserver(PlacesUtils.history, "idle-daily");
-
   // Add a livemark with a visited and an unvisited child
   add_fake_livemark();