diff --git a/browser/base/content/test/about/head.js b/browser/base/content/test/about/head.js
index 1ca560ac63ab..9ff328afb2c4 100644
--- a/browser/base/content/test/about/head.js
+++ b/browser/base/content/test/about/head.js
@@ -161,9 +161,10 @@ function promiseTabLoadEvent(tab, url) {
  * Wait for the search engine to change.
  */
 function promiseContentSearchChange(browser, newEngineName) {
-  return SpecialPowers.spawn(browser, [{ newEngineName }], async function(
-    args
-  ) {
+  // Callers of this depend on very specific, very racy timing, and fail
+  // if we introduce the trip through SpecialPowersParent that
+  // SpecialPowers.spawn requires.
+  return ContentTask.spawn(browser, { newEngineName }, async function(args) {
     return new Promise(resolve => {
       content.addEventListener("ContentSearchService", function listener(
         aEvent
diff --git a/browser/base/content/test/popups/browser_popup_blocker_identity_block.js b/browser/base/content/test/popups/browser_popup_blocker_identity_block.js
index 92ac6561d55b..7051c72abdbb 100644
--- a/browser/base/content/test/popups/browser_popup_blocker_identity_block.js
+++ b/browser/base/content/test/popups/browser_popup_blocker_identity_block.js
@@ -175,12 +175,13 @@ add_task(async function check_permission_state_change() {
   gBrowser.tabContainer.addEventListener("TabOpen", onTabOpen);
 
   // Check if a popup opens.
-  await SpecialPowers.spawn(gBrowser.selectedBrowser, [], async () => {
-    let open = content.document.getElementById("pop");
-    open.click();
-  });
-
-  await BrowserTestUtils.waitForEvent(gBrowser.tabContainer, "TabOpen");
+  await Promise.all([
+    SpecialPowers.spawn(gBrowser.selectedBrowser, [], () => {
+      let open = content.document.getElementById("pop");
+      open.click();
+    }),
+    BrowserTestUtils.waitForEvent(gBrowser.tabContainer, "TabOpen"),
+  ]);
   await BrowserTestUtils.waitForCondition(
     () => popup.linkedBrowser.currentURI.spec != "about:blank"
   );
diff --git a/browser/components/preferences/in-content/tests/siteData/browser_siteData.js b/browser/components/preferences/in-content/tests/siteData/browser_siteData.js
index 932b2239c72e..7f27acc33ba5 100644
--- a/browser/components/preferences/in-content/tests/siteData/browser_siteData.js
+++ b/browser/components/preferences/in-content/tests/siteData/browser_siteData.js
@@ -385,7 +385,7 @@ add_task(async function() {
 
   await openSiteDataSettingsDialog();
 
-  SpecialPowers.spawn(gBrowser.selectedBrowser, [], function() {
+  await SpecialPowers.spawn(gBrowser.selectedBrowser, [], function() {
     let frameDoc = content.gSubDialog._topDialog._frame.contentDocument;
 
     let siteItems = frameDoc.getElementsByTagName("richlistitem");
diff --git a/dom/base/test/browser_bug1554070.js b/dom/base/test/browser_bug1554070.js
index 40e9e6ba739c..342ed3c51579 100644
--- a/dom/base/test/browser_bug1554070.js
+++ b/dom/base/test/browser_bug1554070.js
@@ -37,8 +37,10 @@ add_task(async function() {
 
   // Click the link in file_bug1554070_2.html. It should open example.org in
   // a new tab.
-  await click();
-  await BrowserTestUtils.waitForNewTab(gBrowser, URL2, true);
+  await Promise.all([
+    click(),
+    BrowserTestUtils.waitForNewTab(gBrowser, URL2, true),
+  ]);
   is(gBrowser.tabs.length, 3, "got new tab");
   is(gBrowser.currentURI.spec, URL2, "loaded example.org");