diff --git a/src/aioweb_tls/backends.py b/src/aioweb_tls/backends.py
index 6e497c7..e82e225 100644
--- a/src/aioweb_tls/backends.py
+++ b/src/aioweb_tls/backends.py
@@ -172,9 +172,8 @@ class CurlCffi:
 
         try:
             response = await session.request(method, url, impersonate=impersonate, **kwargs)
-        except aiohttp.ClientError:
-            raise
         except asyncio.TimeoutError:
+            # TimeoutError is an OSError (3.11+): keep it out of the wrap below
             raise
         except OSError as error:
             if _is_timeout_error(error):
@@ -316,9 +315,8 @@ class Noble:
 
         try:
             response = await session.execute_request(method=method.upper(), url=url, **kwargs)
-        except aiohttp.ClientError:
-            raise
         except asyncio.TimeoutError:
+            # TimeoutError is an OSError (3.11+): keep it out of the wrap below
             raise
         except OSError as error:
             if _is_timeout_error(error):