--- a/testing/marionette/harness/marionette_harness/tests/unit/test_window_maximize.py
+++ b/testing/marionette/harness/marionette_harness/tests/unit/test_window_maximize.py
@@ -31,28 +31,26 @@ class TestWindowMaximize(MarionetteTestC
             self.original_size["width"], self.original_size["height"])
 
     def assert_window_maximized(self, actual, delta=None):
         if self.marionette.session_capabilities["platformName"] == "windows_nt":
             delta = 16
         else:
             delta = 8
 
-        self.assertAlmostEqual(
-            actual["width"], self.max["width"],
-            delta=delta,
+        self.assertGreater(
+            actual["width"], self.max["width"] - delta,
             msg="Window width is not within {} px of availWidth: "
                 "current width {} and max width {}"
-                .format(delta, actual["width"], self.max["width"]))
-        self.assertAlmostEqual(
+                .format(delta, actual["width"], self.max["width"] - delta))
+        self.assertGreater(
             actual["height"], self.max["height"],
-            delta=delta,
             msg="Window height is not within {} px of availHeight, "
                 "current height {} and max height {}"
-                .format(delta, actual["height"], self.max["height"]))
+                .format(delta, actual["height"], self.max["height"] - delta))
 
     def assert_window_restored(self, actual):
         self.assertEqual(self.original_size["width"], actual["width"])
         self.assertEqual(self.original_size["height"], actual["height"])
 
     def assert_window_rect(self, rect):
         self.assertIn("width", rect)
         self.assertIn("height", rect)