diff --git a/e2e/browser-v3/arena/bu_real.py b/e2e/browser-v3/arena/bu_real.py
index 6a2dfd0c..ae7b2ae0 100644
--- a/e2e/browser-v3/arena/bu_real.py
+++ b/e2e/browser-v3/arena/bu_real.py
@@ -95,7 +95,9 @@ def reap_leftover_browsers() -> None:
 
 def make_env(task: str, seed: int, max_steps: int):
     patch_launch_with_cdp_port()
-    if "." in task:
+    if task.startswith("compwob."):
+        import compwob  # noqa: F401  registers the composed tasks (legacy-engine base_url)
+    elif "." in task:
         import browsergym.assistantbench  # noqa: F401  lazy: HF datasets machinery breaks playwright
     env_id = f"browsergym/{task}" if "." in task else f"browsergym/miniwob.{task}"
     env = gym.make(env_id, headless=os.environ.get("OSW_ARENA_HEADED") != "1", max_episode_steps=max_steps)
diff --git a/e2e/browser-v3/arena/compwob.py b/e2e/browser-v3/arena/compwob.py
index 951a31a1..be6cc2dd 100644
--- a/e2e/browser-v3/arena/compwob.py
+++ b/e2e/browser-v3/arena/compwob.py
@@ -33,12 +33,18 @@ def compwob_page_names() -> list[str]:
 ALL_COMPWOB_TASKS: list[type] = []
 
 for _name in compwob_page_names():
-    # '../compwob/<name>' rides the miniwob base_url; the browser normalizes the parent hop.
+    # Plain subdomain + a base_url that matches the browser's own URL LITERALLY: validate()
+    # string-compares page.url to base_url+subdomain+'.html', so any '../' cleverness terminates
+    # every episode with 'invalid url' after its first step (measured). Boring URLs are robust URLs.
     _cls = type(
         f"Compwob_{_name.replace('-', '_').replace('.', '_')}",
         (AbstractMiniwobTask,),
-        {"subdomain": f"../compwob/{_name}", "desc": f"CompWoB composed task {_name}"},
+        {"subdomain": _name, "desc": f"CompWoB composed task {_name}"},
     )
+    _orig_init = _cls.__init__
+    def _init(self, seed, base_url=None, _o=_orig_init, **kw):
+        _o(self, seed=seed, base_url=os.environ.get("COMPWOB_URL", "http://localhost:8098/compwob/"), **kw)
+    _cls.__init__ = _init
     # Stable public id: compwob.<name> (the subdomain's ../ prefix stays an URL detail).
     _cls.get_task_id = classmethod(lambda cls, n=_name: f"compwob.{n}")
     ALL_COMPWOB_TASKS.append(_cls)