--- a/dom/animation/EffectCompositor.cpp
+++ b/dom/animation/EffectCompositor.cpp
@@ -103,16 +103,23 @@ IsMatchForCompositor(const KeyframeEffec
     // need to be synchronized with the main thread, run them all there.
     return MatchForCompositor::NoAndBlockThisProperty;
   }
 
   if (!aEffect.HasEffectiveAnimationOfProperty(aProperty)) {
     return MatchForCompositor::No;
   }
 
+  // If we know that the animation is not visible, we don't need to send the
+  // animation to the compositor.
+  if (!aFrame->IsVisibleOrMayHaveVisibleDescendants() ||
+      aFrame->IsScrolledOutOfView()) {
+    return MatchForCompositor::NoAndBlockThisProperty;
+  }
+
   return animation->IsPlaying()
          ? MatchForCompositor::Yes
          : MatchForCompositor::IfNeeded;
 }
 
 // Helper function to factor out the common logic from
 // GetAnimationsForCompositor and HasAnimationsForCompositor.
 //

--- a/dom/animation/test/mozilla/file_restyles.html
+++ b/dom/animation/test/mozilla/file_restyles.html
@@ -130,18 +130,16 @@ function waitForWheelEvent(aTarget) {
                                deltaY: targetRect.height },
                              resolve);
   });
 }
 
 const omtaEnabled = isOMTAEnabled();
 
 const isAndroid = !!navigator.userAgent.includes("Android");
-const isWebRender =
-  SpecialPowers.DOMWindowUtils.layerManagerType == 'WebRender';
 
 function add_task_if_omta_enabled(test) {
   if (!omtaEnabled) {
     info(test.name + " is skipped because OMTA is disabled");
     return;
   }
   add_task(test);
 }
@@ -540,25 +538,17 @@ waitForAllPaints(() => {
   });
 
   add_task_if_omta_enabled(async function no_restyling_compositor_animations_in_visibility_hidden_element() {
     const div = addDiv(null,
      { style: 'animation: opacity 100s; visibility: hidden' });
     const animation = div.getAnimations()[0];
 
     await waitForAnimationReadyToRestyle(animation);
-    if (!isWebRender) {
-      ok(!SpecialPowers.wrap(animation).isRunningOnCompositor);
-    } else {
-      // FIXME: Bug 1456389: The animation should be throttled on the
-      // main-thread (i.e. not to be sent to the compositor)
-      todo(!SpecialPowers.wrap(animation).isRunningOnCompositor,
-           'Animation in visibility:hidden element should NOT be running ' +
-           'on the compositor');
-    }
+    ok(!SpecialPowers.wrap(animation).isRunningOnCompositor);
 
     const markers = await observeStyling(5);
 
     is(markers.length, 0,
        'Animations running on the compositor in visibility hidden element ' +
        'should never cause restyles');
     await ensureElementRemoval(div);
   });