diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml
index 3ad44b2..1b9755c 100644
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@@ -135,6 +135,9 @@ importers:
       ember-source:
         specifier: '>= 3.28'
         version: 5.12.0(@glimmer/component@2.1.1)(@glint/template@1.7.4)(rsvp@4.8.5)(webpack@5.104.1)
+      should-handle-link:
+        specifier: ^1.2.2
+        version: 1.3.0
     devDependencies:
       '@babel/core':
         specifier: ^7.23.6
@@ -8421,6 +8424,7 @@ snapshots:
       '@embroider/addon-shim': 1.10.2
       ember-source: 7.1.0(@glimmer/component@2.1.1)
       qunit: 2.25.0
+      should-handle-link: 1.3.0
     transitivePeerDependencies:
       - '@babel/core'
       - '@glint/template'
diff --git a/test-app/app/templates/application.gts b/test-app/app/templates/application.gts
index 8ac3fb7..a8daeb3 100644
--- a/test-app/app/templates/application.gts
+++ b/test-app/app/templates/application.gts
@@ -7,4 +7,10 @@
   <a href="/does-not-exist">here</a>
   <a href="#title">here</a>
   <a href="/#title">/ here</a>
+
+  {{! non-SPA links: handled by the browser, not the router — visitAllLinks must skip them }}
+  <a href="/foo" target="_blank" rel="noopener noreferrer">new tab</a>
+  <a href="/some-report/index.html" download>download</a>
+  <a href="/foo" rel="external">external</a>
+  <a href="mailto:someone@example.com">email</a>
 </template>
diff --git a/test-app/tests/acceptance/visit-all-links-test.ts b/test-app/tests/acceptance/visit-all-links-test.ts
index 161803e..1bfa216 100644
--- a/test-app/tests/acceptance/visit-all-links-test.ts
+++ b/test-app/tests/acceptance/visit-all-links-test.ts
@@ -20,4 +20,23 @@ module('All Links', function (hooks) {
       `multiple usages does not visit different numbers of links (${size1} === ${size2})`,
     );
   });
+
+  test('non-SPA links are skipped', async function (assert) {
+    // The application template renders target="_blank", download,
+    // rel="external", and mailto: links. The browser handles those natively —
+    // clicking them can never change currentURL() — so a crawl that clicked
+    // them would report failed navigations. Every URL the crawl does visit
+    // must be one the router can serve.
+    const visited: string[] = [];
+
+    await visitAllLinks((url) => {
+      visited.push(url);
+
+      const isNonSPA = url.startsWith('mailto:') || url.endsWith('.html');
+
+      assert.false(isNonSPA, `${url} is a route the router handles`);
+    });
+
+    assert.ok(visited.length > 0, 'the SPA links were still visited');
+  });
 });
diff --git a/test-support/package.json b/test-support/package.json
index 1288cdd..25c89e3 100644
--- a/test-support/package.json
+++ b/test-support/package.json
@@ -53,7 +53,8 @@
   },
   "dependencies": {
     "@ember/test-helpers": "^4.0.4 || ^5.2.2",
-    "@embroider/addon-shim": "^1.8.7"
+    "@embroider/addon-shim": "^1.8.7",
+    "should-handle-link": "^1.2.2"
   },
   "devDependencies": {
     "@babel/core": "^7.23.6",
diff --git a/test-support/src/routing/visit-all.ts b/test-support/src/routing/visit-all.ts
index 843d2e7..2a1febd 100644
--- a/test-support/src/routing/visit-all.ts
+++ b/test-support/src/routing/visit-all.ts
@@ -8,6 +8,7 @@ import {
   findAll,
 } from '@ember/test-helpers';
 import QUnit from 'qunit';
+import { shouldHandle } from 'should-handle-link';
 import type Owner from '@ember/owner';
 import type RouterService from '@ember/routing/router-service';
 
@@ -23,10 +24,29 @@ function findInAppLinks(): InAppLink[] {
   const allAnchorsOnThePage = findAll('a');
 
   for (const a of allAnchorsOnThePage) {
+    // `findAll('a')` can also match SVG `<a>`, whose `href` is an
+    // SVGAnimatedString the router (and shouldHandle) can't work with.
+    if (!(a instanceof HTMLAnchorElement)) continue;
+
     const href = a.getAttribute('href');
 
     if (!href) continue;
-    if (href.startsWith('http')) continue;
+
+    /**
+     * Links the SPA's router never handles are handled natively by the
+     * browser instead (new tab/window via `target`, download dialog,
+     * `mailto:`/`tel:`, cross-origin, `rel="external"`). Clicking them in a
+     * test can't change `currentURL()`, so they'd always be reported as
+     * failed navigations.
+     *
+     * `shouldHandle` is the predicate ember-primitives' @properLinks uses to
+     * decide whether the router handles a click, so the crawler visits
+     * exactly the set of links the router would. The fabricated click event
+     * carries the "plain left click" defaults (button 0, no modifier keys).
+     */
+    if (!shouldHandle(window.location.href, a, new MouseEvent('click'))) {
+      continue;
+    }
 
     const current = new URL(currentURL(), window.location.origin);
     const url = new URL(href, current);