diff --git a/browser/components/urlbar/UrlbarMuxerUnifiedComplete.jsm b/browser/components/urlbar/UrlbarMuxerUnifiedComplete.jsm
index 560c5b4b955b..2f46cd59fea5 100644
--- a/browser/components/urlbar/UrlbarMuxerUnifiedComplete.jsm
+++ b/browser/components/urlbar/UrlbarMuxerUnifiedComplete.jsm
@@ -53,7 +53,8 @@ class MuxerUnifiedComplete extends UrlbarMuxer {
    */
   sort(context) {
     // A Search in a Private Window result should only be shown when there are
-    // other results, and all of them are searches.
+    // other results, and all of them are searches. It should also not be shown
+    // if the user typed an alias, because it's an explicit search engine choice.
     let searchInPrivateWindowIndex = context.results.findIndex(
       r => r.type == UrlbarUtils.RESULT_TYPE.SEARCH && r.payload.inPrivateWindow
     );
@@ -62,7 +63,9 @@ class MuxerUnifiedComplete extends UrlbarMuxer {
       (context.results.length == 1 ||
         context.results.some(
           r =>
-            r.type != UrlbarUtils.RESULT_TYPE.SEARCH || r.payload.keywordOffer
+            r.type != UrlbarUtils.RESULT_TYPE.SEARCH ||
+            r.payload.keywordOffer ||
+            (r.heuristic && r.payload.keyword)
         ))
     ) {
       // Remove the result.
diff --git a/browser/components/urlbar/tests/browser/browser_urlbar_separatePrivateDefault.js b/browser/components/urlbar/tests/browser/browser_urlbar_separatePrivateDefault.js
index 0f98d625e88b..4dd20a5c5bb3 100644
--- a/browser/components/urlbar/tests/browser/browser_urlbar_separatePrivateDefault.js
+++ b/browser/components/urlbar/tests/browser/browser_urlbar_separatePrivateDefault.js
@@ -45,9 +45,17 @@ add_task(async function setup() {
   );
   await Services.search.moveEngine(engine2, 0);
 
+  // Add an engine with an alias.
+  let aliasEngine = await Services.search.addEngineWithDetails("MozSearch", {
+    alias: "alias",
+    method: "GET",
+    template: "http://example.com/?q={searchTerms}",
+  });
+
   registerCleanupFunction(async () => {
     await Services.search.setDefault(oldDefaultEngine);
     await Services.search.setDefaultPrivate(oldDefaultPrivateEngine);
+    await Services.search.removeEngine(aliasEngine);
     await PlacesUtils.history.clear();
   });
 });
@@ -347,3 +355,22 @@ add_task(async function test_oneoff_selected_with_private_engine_keyboard() {
     await BrowserTestUtils.closeWindow(win);
   });
 });
+
+add_task(async function test_alias() {
+  info(
+    "Test that 'Search in a Private Window' doesn's appear if an alias is typed"
+  );
+  await UrlbarTestUtils.promiseAutocompleteResultPopup({
+    window,
+    waitForFocus,
+    value: "alias",
+  });
+  await AssertNoPrivateResult(window);
+
+  await UrlbarTestUtils.promiseAutocompleteResultPopup({
+    window,
+    waitForFocus,
+    value: "alias something",
+  });
+  await AssertNoPrivateResult(window);
+});