diff --git a/httpcore/_backends/anyio.py b/httpcore/_backends/anyio.py
index 288c16b20..286c0e7da 100644
--- a/httpcore/_backends/anyio.py
+++ b/httpcore/_backends/anyio.py
@@ -19,30 +19,12 @@
 from .._utils import is_socket_readable
 from .base import AsyncBackend, AsyncLock, AsyncSemaphore, AsyncSocketStream
 
-# For compatibility with both AnyIO 2.x and 3.x
-# (some functions and context managers were converted from async to sync in 3.0)
-try:
-    from anyio import maybe_async, maybe_async_cm
-except ImportError:
-
-    def maybe_async(x):  # type: ignore
-        return x
-
-    def maybe_async_cm(x):  # type: ignore
-        return x
-
-
-try:
-    from anyio import Lock as create_lock, Semaphore as create_semaphore
-except ImportError:
-    from anyio import create_lock, create_semaphore  # type: ignore
-
 
 class SocketStream(AsyncSocketStream):
     def __init__(self, stream: ByteStream) -> None:
         self.stream = stream
-        self.read_lock = create_lock()
-        self.write_lock = create_lock()
+        self.read_lock = anyio.Lock()
+        self.write_lock = anyio.Lock()
 
     def get_http_version(self) -> str:
         alpn_protocol = self.stream.extra(TLSAttribute.alpn_protocol, None)
@@ -56,7 +38,7 @@ async def start_tls(
     ) -> "SocketStream":
         connect_timeout = timeout.get("connect")
         try:
-            async with maybe_async_cm(anyio.fail_after(connect_timeout)):
+            with anyio.fail_after(connect_timeout):
                 ssl_stream = await TLSStream.wrap(
                     self.stream,
                     ssl_context=ssl_context,
@@ -73,7 +55,7 @@ async def read(self, n: int, timeout: TimeoutDict) -> bytes:
         read_timeout = timeout.get("read")
         async with self.read_lock:
             try:
-                async with maybe_async_cm(anyio.fail_after(read_timeout)):
+                with anyio.fail_after(read_timeout):
                     return await self.stream.receive(n)
             except TimeoutError:
                 raise ReadTimeout from None
@@ -89,7 +71,7 @@ async def write(self, data: bytes, timeout: TimeoutDict) -> None:
         write_timeout = timeout.get("write")
         async with self.write_lock:
             try:
-                async with maybe_async_cm(anyio.fail_after(write_timeout)):
+                with anyio.fail_after(write_timeout):
                     return await self.stream.send(data)
             except TimeoutError:
                 raise WriteTimeout from None
@@ -110,10 +92,10 @@ def is_readable(self) -> bool:
 
 class Lock(AsyncLock):
     def __init__(self) -> None:
-        self._lock = create_lock()
+        self._lock = anyio.Lock()
 
     async def release(self) -> None:
-        await maybe_async(self._lock.release())
+        self._lock.release()
 
     async def acquire(self) -> None:
         await self._lock.acquire()
@@ -127,18 +109,18 @@ def __init__(self, max_value: int, exc_class: type):
     @property
     def semaphore(self) -> anyio.abc.Semaphore:
         if not hasattr(self, "_semaphore"):
-            self._semaphore = create_semaphore(self.max_value)
+            self._semaphore = anyio.Semaphore(self.max_value)
         return self._semaphore
 
     async def acquire(self, timeout: float = None) -> None:
-        async with maybe_async_cm(anyio.move_on_after(timeout)):
+        with anyio.move_on_after(timeout):
             await self.semaphore.acquire()
             return
 
         raise self.exc_class()
 
     async def release(self) -> None:
-        await maybe_async(self.semaphore.release())
+        self.semaphore.release()
 
 
 class AnyIOBackend(AsyncBackend):
@@ -160,7 +142,7 @@ async def open_tcp_stream(
         }
 
         with map_exceptions(exc_map):
-            async with maybe_async_cm(anyio.fail_after(connect_timeout)):
+            with anyio.fail_after(connect_timeout):
                 stream: anyio.abc.ByteStream
                 stream = await anyio.connect_tcp(
                     unicode_host, port, local_host=local_address
@@ -191,7 +173,7 @@ async def open_uds_stream(
         }
 
         with map_exceptions(exc_map):
-            async with maybe_async_cm(anyio.fail_after(connect_timeout)):
+            with anyio.fail_after(connect_timeout):
                 stream: anyio.abc.ByteStream = await anyio.connect_unix(path)
                 if ssl_context:
                     stream = await TLSStream.wrap(
@@ -210,7 +192,7 @@ def create_semaphore(self, max_value: int, exc_class: type) -> AsyncSemaphore:
         return Semaphore(max_value, exc_class=exc_class)
 
     async def time(self) -> float:
-        return await maybe_async(anyio.current_time())
+        return float(anyio.current_time())
 
     async def sleep(self, seconds: float) -> None:
         await anyio.sleep(seconds)
diff --git a/httpcore/_backends/auto.py b/httpcore/_backends/auto.py
index 73d2b4a59..5579ab467 100644
--- a/httpcore/_backends/auto.py
+++ b/httpcore/_backends/auto.py
@@ -17,9 +17,9 @@ def backend(self) -> AsyncBackend:
             backend = sniffio.current_async_library()
 
             if backend == "asyncio":
-                from .asyncio import AsyncioBackend
+                from .anyio import AnyIOBackend
 
-                self._backend_implementation: AsyncBackend = AsyncioBackend()
+                self._backend_implementation: AsyncBackend = AnyIOBackend()
             elif backend == "trio":
                 from .trio import TrioBackend
 
diff --git a/requirements.txt b/requirements.txt
index e62cc3de6..ebdc525a2 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -20,7 +20,7 @@ twine==3.4.1
 wheel==0.36.2
 
 # Tests & Linting
-anyio==3.0.1
+anyio==3.1.0
 autoflake==1.4
 black==21.4b2
 coverage==5.5
diff --git a/setup.py b/setup.py
index 30bd93ba0..09b50baad 100644
--- a/setup.py
+++ b/setup.py
@@ -53,7 +53,7 @@ def get_packages(package):
     packages=get_packages("httpcore"),
     include_package_data=True,
     zip_safe=False,
-    install_requires=["h11>=0.11,<0.13", "sniffio==1.*"],
+    install_requires=["h11>=0.11,<0.13", "sniffio==1.*", "anyio==3.*"],
     extras_require={
         "http2": ["h2>=3,<5"],
     },