diff --git a/html/semantics/popovers/popover-focus.tentative.html b/html/semantics/popovers/popover-focus.tentative.html
index 10c91bcebba7b4..0d35281164c3b9 100644
--- a/html/semantics/popovers/popover-focus.tentative.html
+++ b/html/semantics/popovers/popover-focus.tentative.html
@@ -266,3 +266,83 @@
 
   document.querySelectorAll('body > [popover]').forEach(popover => activateAndVerify(popover));
 </script>
+
+<div id=fixup>
+  <button id=button1>Button1</button>
+  <div popover id=popover1 style="top:100px">
+    <button id=inside_popover1>Inside1</button>
+    <button id=invoker2 popovertoggletarget=popover2>Nested Invoker 2</button>
+    <button id=inside_popover2>Inside2</button>
+  </div>
+  <button id=button2>Button2</button>
+  <button popovertoggletarget=popover1 id=invoker1>Invoker1</button>
+  <button id=button3>Button3</button>
+  <div popover id=popover2 style="top:200px">
+    <button id=inside_popover3>Inside3</button>
+    <button id=invoker3 popovertoggletarget=popover3>Nested Invoker 3</button>
+  </div>
+  <div popover id=popover3 style="top:300px">
+    Non-focusable popover
+  </div>
+  <button id=button4>Button4</button>
+</div>
+<style>
+  #fixup [popover] {
+    bottom:auto;
+  }
+</style>
+<script>
+async function verifyFocusOrder(order) {
+  order[0].focus();
+  for(let i=0;i<order.length;++i) {
+    const control = order[i];
+    assert_equals(document.activeElement,control,`Step ${i+1}`);
+    await sendTab();
+  }
+  // Shift-tab not supported, crbug.com/893480.
+  // for(let i=order.length-1;i>=0;--i) {
+  //   const control = order[i];
+  //   await sendShiftTab();
+  //   assert_equals(document.activeElement,control,`Step ${i+1} (backwards)`);
+  // }
+}
+promise_test(async t => {
+  button1.focus();
+  assert_equals(document.activeElement,button1);
+  await sendTab();
+  assert_equals(document.activeElement,button2,'Hidden popover should be skipped');
+  // Shift-tab not supported, crbug.com/893480.
+  // await sendShiftTab();
+  // assert_equals(document.activeElement,button1,'Hidden popover should be skipped backwards');
+  //await sendTab();
+  await sendTab();
+  assert_equals(document.activeElement,invoker1);
+  await sendEnter(); // Activate the invoker
+  assert_true(popover1.matches(':open'), 'popover1 should be invoked by invoker1');
+  assert_equals(document.activeElement,invoker1,'Focus should not move when popover is shown');
+  await sendTab();
+  assert_equals(document.activeElement,inside_popover1,'Focus should move from invoker into the open popover');
+  await sendTab();
+  assert_equals(document.activeElement,invoker2,'Focus should move within popover');
+  await verifyFocusOrder([button1, button2, invoker1, inside_popover1, invoker2, inside_popover2, button3, button4]);
+  invoker2.focus();
+  await sendEnter(); // Activate the nested invoker
+  assert_true(popover2.matches(':open'), 'popover2 should be invoked by nested invoker');
+  assert_equals(document.activeElement,invoker2,'Focus should stay on the invoker');
+  await sendTab();
+  assert_equals(document.activeElement,inside_popover3,'Focus should move into nested popover');
+  await sendTab();
+  assert_equals(document.activeElement,invoker3);
+  await sendEnter(); // Activate the (empty) nested invoker
+  assert_true(popover3.matches(':open'), 'popover3 should be invoked by nested invoker');
+  assert_equals(document.activeElement,invoker3,'Focus should stay on the invoker');
+  await sendTab();
+  assert_equals(document.activeElement,inside_popover2,'Focus should skip popover without focusable content, going back to higher scope');
+  await sendTab();
+  assert_equals(document.activeElement,button3,'Focus should exit popovers');
+  await sendTab();
+  assert_equals(document.activeElement,button4,'Focus should skip popovers');
+  button1.focus();
+  await verifyFocusOrder([button1, button2, invoker1, inside_popover1, invoker2, inside_popover3, invoker3, inside_popover2, button3, button4]);
+}, "Popover focus navigation");
+</script>
diff --git a/html/semantics/popovers/popover-light-dismiss.tentative.html b/html/semantics/popovers/popover-light-dismiss.tentative.html
index 2581ca6fdeea0f..2a101483cb8c8e 100644
--- a/html/semantics/popovers/popover-light-dismiss.tentative.html
+++ b/html/semantics/popovers/popover-light-dismiss.tentative.html
@@ -389,41 +389,6 @@
   },'Moving focus back to the anchor element should not dismiss the popover');
 </script>
 
-<div popover id=p9>
-  <button>Button</button>
-  <span id=inside9after>Inside popover 9 after button</span>
-</div>
-<button id=b9after popovertoggletarget='p9'>Popover 9</button>
-<script>
-  promise_test(async () => {
-    const popover9 = document.querySelector('#p9');
-    const inside9After = document.querySelector('#inside9after');
-    const popover9Invoker = document.querySelector('#b9after');
-    assert_false(popover9.matches(':open'));
-    popover9Invoker.click(); // Trigger via the button
-    await clickOn(inside9After);
-    assert_true(popover9.matches(':open'));
-    await sendTab();
-    assert_equals(document.activeElement,popover9Invoker,'Focus should move to the invoking element');
-    assert_true(popover9.matches(':open'),'popover should stay open');
-    popover9.hidePopover();
-  },'Moving focus back to the active trigger element should not dismiss the popover');
-
-  promise_test(async () => {
-    const popover9 = document.querySelector('#p9');
-    const inside9After = document.querySelector('#inside9after');
-    const popover9Invoker = document.querySelector('#b9after');
-    assert_false(popover9.matches(':open'));
-    popover9.showPopover(); // Trigger directly
-    await clickOn(inside9After);
-    assert_true(popover9.matches(':open'));
-    await sendTab();
-    assert_equals(document.activeElement,popover9Invoker,'Focus should move to the invoking element');
-    assert_true(popover9.matches(':open'),'popover should stay open - even though the trigger wasn\'t used, it points to this popover');
-  },'Moving focus back to an inactive trigger element should also *not* dismiss the popover');
-</script>
-
-
 <!-- Convoluted ancestor relationship -->
 <div popover id=convoluted_p1>Popover 1
   <div id=convoluted_anchor>Anchor
diff --git a/html/semantics/popovers/resources/popover-utils.js b/html/semantics/popovers/resources/popover-utils.js
index 8f66dc0844975d..efc318b3c9fd34 100644
--- a/html/semantics/popovers/resources/popover-utils.js
+++ b/html/semantics/popovers/resources/popover-utils.js
@@ -12,14 +12,33 @@ async function clickOn(element) {
 }
 async function sendTab() {
   await waitForRender();
-  await new test_driver.send_keys(document.body,'\uE004'); // Tab
-  await waitForRender();
-}
+  const kTab = '\uE004';
+  await new test_driver.send_keys(document.body,kTab);
+  await waitForRender();
+}
+// Waiting for crbug.com/893480:
+// async function sendShiftTab() {
+//   await waitForRender();
+//   const kShift = '\uE008';
+//   const kTab = '\uE004';
+//   await new test_driver.Actions()
+//     .keyDown(kShift)
+//     .keyDown(kTab)
+//     .keyUp(kTab)
+//     .keyUp(kShift)
+//     .send();
+//   await waitForRender();
+// }
 async function sendEscape() {
   await waitForRender();
   await new test_driver.send_keys(document.body,'\uE00C'); // Escape
   await waitForRender();
 }
+async function sendEnter() {
+  await waitForRender();
+  await new test_driver.send_keys(document.body,'\uE007'); // Enter
+  await waitForRender();
+}
 function isElementVisible(el) {
   return !!(el.offsetWidth || el.offsetHeight || el.getClientRects().length);
 }