diff --git a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.html b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html
similarity index 75%
rename from testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.html
rename to testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html
index f6d7f26ce83c1..d3e9956368a5c 100644
--- a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.html
+++ b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html
@@ -6,6 +6,7 @@
 <link rel="author" title="Domenic Denicola" href="mailto:d@domenic.me">
 <script src="/resources/testharness.js"></script>
 <script src="/resources/testharnessreport.js"></script>
+<script src="/common/utils.js"></script> <!-- Use token() to allow running tests in parallel -->
 
 <div id="log"></div>
 
@@ -13,23 +14,19 @@
 "use strict";
 
 promise_test(t => {
+  const channelName = token();
   return Promise.all([
-    createIFrame("resources/broadcastchannel-iframe.html"),
-    createIFrame("resources/broadcastchannel-iframe.html"),
-    createIFrame("resources/broadcastchannel-iframe.html")
+    createIFrame(`resources/broadcastchannel-iframe.html?channel=${channelName}&index=0`),
+    createIFrame(`resources/broadcastchannel-iframe.html?channel=${channelName}&index=1`),
+    createIFrame(`resources/broadcastchannel-iframe.html?channel=${channelName}&index=2`)
   ]).then(() => {
     const sab = new SharedArrayBuffer(3);
     const view = new Uint8Array(sab);
-    const channel = new BroadcastChannel("channel name");
+    const channel = new BroadcastChannel(channelName);
 
     return new Promise(resolve => {
       let soFar = 0;
-      channel.onmessage = t.step_func(({ data: { sab: broadcastSAB, i } }) => {
-        if (broadcastSAB) {
-          // We only care about "broadcasts" from the workers.
-          return;
-        }
-
+      channel.onmessage = t.step_func(({ data: { i } }) => {
         assert_in_array(i, [0, 1, 2], "Any message events must come from expected sources");
         ++soFar;
 
diff --git a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html.headers b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html.headers
new file mode 100644
index 0000000000000..63b60e490f47f
--- /dev/null
+++ b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/broadcastchannel-success.https.html.headers
@@ -0,0 +1,2 @@
+Cross-Origin-Opener-Policy: same-origin
+Cross-Origin-Embedder-Policy: require-corp
diff --git a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html
index 792d6fd201380..02b9bcbbe8827 100644
--- a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html
+++ b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html
@@ -4,10 +4,13 @@
 
 <script>
 "use strict";
-const channel = new BroadcastChannel("channel name");
+const query = new URLSearchParams(location.search);
+const channel = new BroadcastChannel(query.get("channel"));
+const i = Number(query.get("index"));
 
-channel.onmessage = ({ data: { sab, i }, source }) => {
-  if (!sab) {
+channel.onmessage = e => {
+  const sab = e.data.sab;
+  if (sab === undefined) {
     // We only care about "broadcasts" from the window
     return;
   }
diff --git a/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html.headers b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html.headers
new file mode 100644
index 0000000000000..6604450991a12
--- /dev/null
+++ b/testing/web-platform/tests/html/infrastructure/safe-passing-of-structured-data/shared-array-buffers/resources/broadcastchannel-iframe.html.headers
@@ -0,0 +1 @@
+Cross-Origin-Embedder-Policy: require-corp