diff --git a/datasette/app.py b/datasette/app.py
index be507241..09936b3a 100644
--- a/datasette/app.py
+++ b/datasette/app.py
@@ -2150,11 +2150,6 @@ class DatasetteRouter:
         context = {}
         if path.endswith(b"/"):
             path = path.rstrip(b"/")
-
-            # If you redirect with a // at the beginning, you end up with an open redirect, so
-            # https://my.site//foo/ - will redirect to https://foo
-            path = re.sub(rb"^/+", b"/", path)
-
             if request.scope["query_string"]:
                 path += b"?" + request.scope["query_string"]
             await asgi_send_redirect(send, path.decode("latin1"))
diff --git a/datasette/utils/asgi.py b/datasette/utils/asgi.py
index 40214cbe..7f3329a6 100644
--- a/datasette/utils/asgi.py
+++ b/datasette/utils/asgi.py
@@ -6,6 +6,7 @@ from pathlib import Path
 from http.cookies import SimpleCookie, Morsel
 import aiofiles
 import aiofiles.os
+import re
 
 # Workaround for adding samesite support to pre 3.8 python
 Morsel._reserved["samesite"] = "SameSite"
@@ -248,6 +249,9 @@ async def asgi_send_html(send, html, status=200, headers=None):
 
 
 async def asgi_send_redirect(send, location, status=302):
+    # Prevent open redirect vulnerability: strip multiple leading slashes
+    # //example.com would be interpreted as a protocol-relative URL (e.g., https://example.com/)
+    location = re.sub(r"^/+", "/", location)
     await asgi_send(
         send,
         "",
diff --git a/tests/test_custom_pages.py b/tests/test_custom_pages.py
index ccc139ce..39a4c06b 100644
--- a/tests/test_custom_pages.py
+++ b/tests/test_custom_pages.py
@@ -100,6 +100,7 @@ def test_custom_route_pattern_404(custom_pages_client):
 
 
 def test_custom_route_pattern_with_slash_slash_302(custom_pages_client):
-    response = custom_pages_client.get("//nastyOpenRedirect/")
+    # https://github.com/simonw/datasette/issues/2429
+    response = custom_pages_client.get("//example.com/")
     assert response.status == 302
-    assert response.headers["location"] == "/nastyOpenRedirect"
+    assert response.headers["location"] == "/example.com"