--- a/devtools/client/styleeditor/test/browser.ini
+++ b/devtools/client/styleeditor/test/browser.ini
@@ -85,16 +85,18 @@ fail-if = fission # Got the expected num
 [browser_styleeditor_bug_851132_middle_click.js]
 [browser_styleeditor_bug_870339.js]
 [browser_styleeditor_bug_1405342_serviceworker_iframes.js]
 [browser_styleeditor_copyurl.js]
 [browser_styleeditor_enabled.js]
 [browser_styleeditor_fetch-from-netmonitor.js]
 fail-if = fission
 [browser_styleeditor_filesave.js]
+[browser_styleeditor_fission_switch_target.js]
+skip-if = true # Bug 1604126
 [browser_styleeditor_highlight-selector.js]
 [browser_styleeditor_import.js]
 [browser_styleeditor_import_rule.js]
 [browser_styleeditor_init.js]
 [browser_styleeditor_inline_friendly_names.js]
 [browser_styleeditor_loading.js]
 [browser_styleeditor_loading_with_containers.js]
 [browser_styleeditor_media_sidebar.js]

new file mode 100644
--- /dev/null
+++ b/devtools/client/styleeditor/test/browser_styleeditor_fission_switch_target.js
@@ -0,0 +1,28 @@
+/* Any copyright is dedicated to the Public Domain.
+   http://creativecommons.org/publicdomain/zero/1.0/ */
+"use strict";
+
+// Test switching for the top-level target.
+
+const PARENT_PROCESS_URI = "about:robots";
+const CONTENT_PROCESS_URI = TEST_BASE_HTTPS + "simple.html";
+
+add_task(async function() {
+  await pushPref("devtools.target-switching.enabled", true);
+
+  // We use about:robots, because this page will run in the parent process.
+  // Navigating from about:robots to a regular content page will always trigger a target
+  // switch, with or without fission.
+
+  info("Open a page that runs in the parent process");
+  const { toolbox, ui } = await openStyleEditorForURL(PARENT_PROCESS_URI);
+  is(ui.editors.length, 3, `Three style sheets for ${PARENT_PROCESS_URI}`);
+
+  info("Navigate to a page that runs in the child process");
+  await navigateToAndWaitForStyleSheets(CONTENT_PROCESS_URI, ui);
+  is(ui.editors.length, 2, `Two sheets present for ${CONTENT_PROCESS_URI}`);
+
+  const onToolboxDestroyed = gDevTools.once("toolbox-destroyed");
+  toolbox.closeToolbox();
+  await onToolboxDestroyed;
+});