diff --git a/httpcore/__init__.py b/httpcore/__init__.py
index 330745a5d..014213bae 100644
--- a/httpcore/__init__.py
+++ b/httpcore/__init__.py
@@ -130,7 +130,7 @@ def __init__(self, *args, **kwargs):  # type: ignore
     "WriteError",
 ]
 
-__version__ = "1.0.6"
+__version__ = "1.0.5"
 
 
 __locals = locals()
diff --git a/httpcore/_synchronization.py b/httpcore/_synchronization.py
index 2d86f8b8e..8d8c5b689 100644
--- a/httpcore/_synchronization.py
+++ b/httpcore/_synchronization.py
@@ -1,4 +1,5 @@
 import asyncio
+import sys
 import threading
 from types import TracebackType
 from typing import (
@@ -29,6 +30,18 @@
     anyio = None  # type: ignore
 
 
+if sys.version_info >= (3, 11):  # pragma: nocover
+    import asyncio as asyncio_timeout
+
+    anyio_shield = None
+else:  # pragma: nocover
+    import async_timeout as asyncio_timeout
+
+    if anyio is None:  # pragma: nocover
+        raise RuntimeError("Running in Python<3.11 requires anyio")
+    anyio_shield = anyio.CancelScope
+
+
 AsyncBackend = Literal["asyncio", "trio"]
 
 
@@ -163,9 +176,11 @@ async def wait(self, timeout: Optional[float] = None) -> None:
                 with trio.fail_after(timeout_or_inf):
                     await event.wait()
         else:
-            asyncio_exc_map: ExceptionMapping = {TimeoutError: PoolTimeout}
+            asyncio_exc_map: ExceptionMapping = {
+                asyncio.exceptions.TimeoutError: PoolTimeout
+            }
             with map_exceptions(asyncio_exc_map):
-                async with asyncio.timeout(timeout):
+                async with asyncio_timeout.timeout(timeout):
                     await event.wait()
 
 
@@ -217,8 +232,11 @@ async def shield(shielded: Callable[[], Coroutine[Any, Any, None]]) -> None:
         if current_async_backend() == "trio":
             with trio.CancelScope(shield=True):
                 await shielded()
+        elif sys.version_info < (3, 11):  # pragma: nocover
+            with anyio_shield(shield=True):
+                await shielded()
         else:
-            await AsyncShieldCancellation._asyncio_shield(shielded)
+            await AsyncShieldCancellation._asyncio_shield(shielded)  # pragma: nocover
 
     @staticmethod
     async def _asyncio_shield(
@@ -227,7 +245,7 @@ async def _asyncio_shield(
         inner_task = asyncio.create_task(shielded())
         try:
             await asyncio.shield(inner_task)
-        except asyncio.CancelledError:
+        except (asyncio.exceptions.CancelledError, asyncio.CancelledError):
             # Let the inner_task to complete as it was shielded from the cancellation
             await inner_task
 
diff --git a/pyproject.toml b/pyproject.toml
index 85c787402..7a9fea162 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -31,6 +31,7 @@ classifiers = [
 dependencies = [
     "certifi",
     "h11>=0.13,<0.15",
+    "async-timeout==4.*; python_version < '3.11'",
 ]
 
 [project.optional-dependencies]
diff --git a/tests/conftest.py b/tests/conftest.py
deleted file mode 100644
index 463a189c0..000000000
--- a/tests/conftest.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import pytest
-
-
-@pytest.fixture(
-    params=[
-        pytest.param(("asyncio", {"httpcore_use_anyio": False}), id="asyncio"),
-        pytest.param(("asyncio", {"httpcore_use_anyio": True}), id="asyncio+anyio"),
-        pytest.param(("trio", {}), id="trio"),
-    ]
-)
-def anyio_backend(request, monkeypatch):
-    backend_name, options = request.param
-    options = {**options}
-    use_anyio = options.pop("httpcore_use_anyio", False)
-    monkeypatch.setenv("HTTPCORE_PREFER_ANYIO", "1" if use_anyio else "0")
-    return backend_name, options