diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 3f063517..6ef9d5cd 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -24,6 +24,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
   object with a new one rather than clear the old one.
 - **BACKWARDS INCOMPATIBLE** Removed the ``anyio.create_queue`` function and the ``Queue`` class.
   Use memory object streams instead.
+- **BACKWARDS INCOMPATIBLE** Renamed the ``max_size`` parameter to ``max_bytes`` wherever it
+  occurred (this was inconsistently named ``max_bytes`` in some subclasses before)
 - Unified checkpoint behavior: a cancellation check now calls ``sleep(0)`` on asyncio and curio,
   allowing the scheduler to switch to a different task
 - Added memory object streams
diff --git a/src/anyio/_networking.py b/src/anyio/_networking.py
index 54d83e07..2d508ba1 100644
--- a/src/anyio/_networking.py
+++ b/src/anyio/_networking.py
@@ -259,7 +259,7 @@ async def receive_exactly(self, nbytes: int) -> bytes:
         self._buffer = self._buffer[nbytes:]
         return result
 
-    async def receive_until(self, delimiter: bytes, max_size: int) -> bytes:
+    async def receive_until(self, delimiter: bytes, max_bytes: int) -> bytes:
         delimiter_size = len(delimiter)
         offset = 0
         while True:
@@ -271,11 +271,11 @@ async def receive_until(self, delimiter: bytes, max_size: int) -> bytes:
                 return found
 
             # Check if the buffer is already at or over the limit
-            if len(self._buffer) >= max_size:
-                raise DelimiterNotFound(max_size)
+            if len(self._buffer) >= max_bytes:
+                raise DelimiterNotFound(max_bytes)
 
             # Read more data into the buffer from the socket
-            read_size = max_size - len(self._buffer)
+            read_size = max_bytes - len(self._buffer)
             data = await self._socket.recv(read_size)
             if not data:
                 raise IncompleteRead
@@ -284,9 +284,9 @@ async def receive_until(self, delimiter: bytes, max_size: int) -> bytes:
             offset = max(len(self._buffer) - delimiter_size + 1, 0)
             self._buffer += data
 
-    async def receive_chunks(self, max_size: int):
+    async def receive_chunks(self, max_bytes: int):
         while True:
-            data = await self.receive(max_size)
+            data = await self.receive(max_bytes)
             if data:
                 yield data
             else:
@@ -447,9 +447,9 @@ async def receive(self, max_bytes: int) -> Tuple[bytes, Tuple[str, int]]:
         data, addr = await self._socket.recvfrom(max_bytes)
         return data, addr[:2]
 
-    async def receive_packets(self, max_size: int):
+    async def receive_packets(self, max_bytes: int):
         while self._socket.fileno() != -1:
-            packet, address = await self.receive(max_size)
+            packet, address = await self.receive(max_bytes)
             if packet:
                 yield (packet, address)
             else:
diff --git a/src/anyio/abc/networking.py b/src/anyio/abc/networking.py
index cc3c65cf..a281c808 100644
--- a/src/anyio/abc/networking.py
+++ b/src/anyio/abc/networking.py
@@ -271,12 +271,13 @@ async def receive(self, max_bytes: int) -> Tuple[bytes, Tuple[str, int]]:
         """
 
     @abstractmethod
-    def receive_packets(self, max_size: int) -> AsyncIterable[Tuple[bytes, str]]:
+    def receive_packets(self, max_bytes: int) -> AsyncIterable[Tuple[bytes, str]]:
         """
         Return an async iterable which yields packets read from the socket.
 
         The iterable exits if the socket is closed.
 
+        :param max_bytes: maximum number of bytes to return
         :return: an async iterable yielding (bytes, source address) tuples
         """