diff --git a/README.rst b/README.rst
index 72fb3337..9bf6d31e 100644
--- a/README.rst
+++ b/README.rst
@@ -112,6 +112,21 @@ should start with a slash, but not end with one; for example::
     daphne --root-path=/forum django_project.asgi:application
 
 
+Permessage compression
+----------------------
+
+Daphne supports and by default accepts  ``permessage-deflate`` compression
+(`permessage-deflate specification <http://tools.ietf.org/html/draft-ietf-hybi-permessage-compression>`_).
+Additional ``permessage-bzip2``, ``permessage-snappy`` compressions will be also enabled by default if
+``bz2`` and `snappy <https://snappy.math.uic.edu/>`_ python packages are available in daphne environment.
+The compression implementation is provided by
+`Autobahn|Python <https://github.com/crossbario/autobahn-python>`_ package, see:
+`permessage-deflate <https://github.com/crossbario/autobahn-python/blob/master/autobahn/websocket/compress_deflate.py>`_,
+`permessage-bzip2 <https://github.com/crossbario/autobahn-python/blob/master/autobahn/websocket/compress_bzip2.py>`_,
+`permessage-snappy <https://github.com/crossbario/autobahn-python/blob/master/autobahn/websocket/compress_snappy.py>`_.
+
+
+
 Python Support
 --------------
 
diff --git a/daphne/server.py b/daphne/server.py
index 5ede8082..402142b7 100755
--- a/daphne/server.py
+++ b/daphne/server.py
@@ -23,6 +23,7 @@
 import time
 from concurrent.futures import CancelledError
 
+from autobahn.websocket.compress import PERMESSAGE_COMPRESSION_EXTENSION as EXTENSIONS
 from twisted.internet import defer, reactor
 from twisted.internet.endpoints import serverFromString
 from twisted.logger import STDLibLogObserver, globalLogBeginner
@@ -44,6 +45,11 @@ def __init__(
         http_timeout=None,
         websocket_timeout=86400,
         websocket_connect_timeout=20,
+        websocket_permessage_compression_extensions=(
+            "permessage-deflate",
+            "permessage-bzip2",
+            "permessage-snappy",
+        ),
         ping_interval=20,
         ping_timeout=30,
         root_path="",
@@ -73,6 +79,9 @@ def __init__(
         self.websocket_timeout = websocket_timeout
         self.websocket_connect_timeout = websocket_connect_timeout
         self.websocket_handshake_timeout = websocket_handshake_timeout
+        self.websocket_permessage_compression_extensions = (
+            websocket_permessage_compression_extensions
+        )
         self.application_close_timeout = application_close_timeout
         self.root_path = root_path
         self.verbosity = verbosity
@@ -94,6 +103,7 @@ def run(self):
             autoPingTimeout=self.ping_timeout,
             allowNullOrigin=True,
             openHandshakeTimeout=self.websocket_handshake_timeout,
+            perMessageCompressionAccept=self.accept_permessage_compression_extension,
         )
         if self.verbosity <= 1:
             # Redirect the Twisted log to nowhere
@@ -246,6 +256,21 @@ def check_headers_type(message):
                     )
                 )
 
+    def accept_permessage_compression_extension(self, offers):
+        """
+        Accepts websocket compression extension as required by `autobahn` package.
+        """
+        for offer in offers:
+            for ext in self.websocket_permessage_compression_extensions:
+                if ext in EXTENSIONS and isinstance(offer, EXTENSIONS[ext]["Offer"]):
+                    return EXTENSIONS[ext]["OfferAccept"](offer)
+                elif ext not in EXTENSIONS:
+                    logger.warning(
+                        "Compression extension %s could not be accepted. "
+                        "It is not supported or a dependency is missing.",
+                        ext,
+                    )
+
     ### Utility
 
     def application_checker(self):
diff --git a/daphne/ws_protocol.py b/daphne/ws_protocol.py
index 1962450d..10d62bfd 100755
--- a/daphne/ws_protocol.py
+++ b/daphne/ws_protocol.py
@@ -182,7 +182,7 @@ def handle_reply(self, message):
         if "type" not in message:
             raise ValueError("Message has no type defined")
         if message["type"] == "websocket.accept":
-            self.serverAccept(message.get("subprotocol", None))
+            self.serverAccept(message.get("subprotocol", None), message.get("headers", None))
         elif message["type"] == "websocket.close":
             if self.state == self.STATE_CONNECTING:
                 self.serverReject()
@@ -214,11 +214,15 @@ def handle_exception(self, exception):
         else:
             self.sendCloseFrame(code=1011)
 
-    def serverAccept(self, subprotocol=None):
+    def serverAccept(self, subprotocol=None, headers=None):
         """
         Called when we get a message saying to accept the connection.
         """
-        self.handshake_deferred.callback(subprotocol)
+        if headers is None:
+            self.handshake_deferred.callback(subprotocol)
+        else:
+            headers_dict = {key.decode(): value.decode() for key, value in headers}
+            self.handshake_deferred.callback((subprotocol, headers_dict))
         del self.handshake_deferred
         logger.debug("WebSocket %s accepted by application", self.client_addr)