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diff --git a/dom/animation/test/mozilla/file_deferred_start.html b/dom/animation/test/mozilla/file_deferred_start.html
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+++ b/dom/animation/test/mozilla/file_deferred_start.html
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+<!doctype html>
+<meta charset=utf-8>
+<script src="../testcommon.js"></script>
+<script src="/tests/SimpleTest/paint_listener.js"></script>
+<style>
+@keyframes empty { }
+.target {
+  /* Element needs geometry to be eligible for layerization */
+  width: 100px;
+  height: 100px;
+  background-color: white;
+}
+</style>
+<body>
+<script>
+'use strict';
+
+function waitForDocLoad() {
+  return new Promise((resolve, reject) => {
+    if (document.readyState === 'complete') {
+      resolve();
+    } else {
+      window.addEventListener('load', resolve);
+    }
+  });
+}
+
+function waitForPaints() {
+  return new Promise((resolve, reject) => {
+    waitForAllPaintsFlushed(resolve);
+  });
+}
+
+promise_test(async t => {
+  // Test that empty animations actually start.
+  //
+  // Normally we tie the start of animations to when their first frame of
+  // the animation is rendered. However, for animations that don't actually
+  // trigger a paint (e.g. because they are empty, or are animating something
+  // that doesn't render or is offscreen) we want to make sure they still
+  // start.
+  //
+  // Before we start, wait for the document to finish loading, then create
+  // div element, and wait for painting. This is because during loading we will
+  // have other paint events taking place which might, by luck, happen to
+  // trigger animations that otherwise would not have been triggered, leading to
+  // false positives.
+  //
+  // As a result, it's better to wait until we have a more stable state before
+  // continuing.
+  await waitForDocLoad();
+
+  const div = addDiv(t);
+
+  await waitForPaints();
+
+  div.style.animation = 'empty 1000s';
+  const animation = div.getAnimations()[0];
+
+  let promiseCallbackDone = false;
+  animation.ready.then(() => {
+    promiseCallbackDone = true;
+  }).catch(() => {
+    assert_unreached('ready promise was rejected');
+  });
+
+  // We need to wait for up to three frames. This is because in some
+  // cases it can take up to two frames for the initial layout
+  // to take place. Even after that happens we don't actually resolve the
+  // ready promise until the following tick.
+  await waitForAnimationFrames(3);
+
+  assert_true(promiseCallbackDone,
+              'ready promise for an empty animation was resolved'
+              + ' within three animation frames');
+}, 'Animation.ready is resolved for an empty animation');
+
+// Test that compositor animations with delays get synced correctly
+//
+// NOTE: It is important that we DON'T use
+// SpecialPowers.DOMWindowUtils.advanceTimeAndRefresh here since that takes
+// us through a different code path.
+promise_test(async t => {
+  assert_false(SpecialPowers.DOMWindowUtils.isTestControllingRefreshes,
+               'Test should run without the refresh driver being under'
+               + ' test control');
+
+  // This test only applies to compositor animations
+  if (!isOMTAEnabled()) {
+    return;
+  }
+
+  const div = addDiv(t, { class: 'target' });
+
+  // As with the above test, any stray paints can cause this test to produce
+  // a false negative (that is, pass when it should fail). To avoid this we
+  // wait for paints and only then do we commence the test.
+  await waitForPaints();
+
+  const animation =
+    div.animate({ transform: [ 'translate(0px)', 'translate(100px)' ] },
+                { duration: 400 * MS_PER_SEC,
+                  delay: -200 * MS_PER_SEC });
+
+  await waitForAnimationReadyToRestyle(animation);
+
+  await waitForPaints();
+
+  const transformStr =
+    SpecialPowers.DOMWindowUtils.getOMTAStyle(div, 'transform');
+  const translateX = getTranslateXFromTransform(transformStr);
+
+  // If the delay has been applied we should be about half-way through
+  // the animation. However, if we applied it twice we will be at the
+  // end of the animation already so check that we are roughly half way
+  // through.
+  assert_between_inclusive(translateX, 40, 75,
+      'Animation is about half-way through on the compositor');
+}, 'Starting an animation with a delay starts from the correct point');
+
+// Test that compositor animations with a playback rate start at the
+// appropriate point.
+//
+// NOTE: As with the previous test, it is important that we DON'T use
+// SpecialPowers.DOMWindowUtils.advanceTimeAndRefresh here since that takes
+// us through a different code path.
+promise_test(async t => {
+  assert_false(SpecialPowers.DOMWindowUtils.isTestControllingRefreshes,
+               'Test should run without the refresh driver being under'
+               + ' test control');
+
+  // This test only applies to compositor animations
+  if (!isOMTAEnabled()) {
+    return;
+  }
+
+  const div = addDiv(t, { class: 'target' });
+
+  // Wait for the document to load and painting (see notes in previous test).
+  await waitForPaints();
+
+  const animation =
+    div.animate({ transform: [ 'translate(0px)', 'translate(100px)' ] },
+                200 * MS_PER_SEC);
+  animation.currentTime = 100 * MS_PER_SEC;
+  animation.playbackRate = 0.1;
+
+  await waitForPaints();
+
+  const transformStr =
+    SpecialPowers.DOMWindowUtils.getOMTAStyle(div, 'transform');
+  const translateX = getTranslateXFromTransform(transformStr);
+
+  // We pass the playback rate to the compositor independently and we have
+  // tests to ensure that it is correctly applied there. However, if, when
+  // we resolve the start time of the pending animation, we fail to
+  // incorporate the playback rate, we will end up starting from the wrong
+  // point and the current time calculated on the compositor will be wrong.
+  assert_between_inclusive(translateX, 25, 75,
+      'Animation is about half-way through on the compositor');
+}, 'Starting an animation with a playbackRate starts from the correct point');
+
+function getTranslateXFromTransform(transformStr) {
+  const matrixComponents =
+    transformStr.startsWith('matrix(')
+    ? transformStr.substring('matrix('.length, transformStr.length-1)
+                  .split(',')
+                  .map(component => Number(component))
+    : [];
+  assert_equals(matrixComponents.length, 6,
+                'Got a valid transform matrix on the compositor'
+                + ' (got: "' + transformStr + '")');
+
+  return matrixComponents[4];
+}
+
+done();
+</script>
+</body>