diff --git a/docs/project/changelog.rst b/docs/project/changelog.rst
index 738288e4..59ccb15a 100644
--- a/docs/project/changelog.rst
+++ b/docs/project/changelog.rst
@@ -44,6 +44,14 @@ Improvements
 * :func:`~asyncio.client.connect` now closes connections with close code 1011
   (internal error) when exiting the context manager with an exception.
 
+Bug fixes
+.........
+
+* Negotiating ``permessage-deflate`` no longer fails with a :exc:`ValueError`
+  when the peer asks for a window of 8 bits on the side that compresses.
+  :mod:`zlib` cannot create a raw deflate compressor with such a window, so
+  the extension is declined instead.
+
 .. _17.1:
 
 17.1
diff --git a/src/websockets/extensions/permessage_deflate.py b/src/websockets/extensions/permessage_deflate.py
index 50276637..0c926f69 100644
--- a/src/websockets/extensions/permessage_deflate.py
+++ b/src/websockets/extensions/permessage_deflate.py
@@ -464,6 +464,12 @@ def process_response_params(
             elif client_max_window_bits > self.client_max_window_bits:
                 raise NegotiationError("unsupported client_max_window_bits")
 
+        # zlib cannot build a raw deflate compressor with an 8 bit window, so
+        # 8 is unusable for the window we compress with, even though it is a
+        # legal value on the wire and fine for the window we decompress with.
+        if client_max_window_bits == 8:
+            raise NegotiationError("unsupported client_max_window_bits")
+
         return PerMessageDeflate(
             server_no_context_takeover,  # remote_no_context_takeover
             client_no_context_takeover,  # local_no_context_takeover
@@ -658,6 +664,13 @@ def process_request_params(
             elif self.client_max_window_bits < client_max_window_bits:
                 client_max_window_bits = self.client_max_window_bits
 
+        # zlib cannot build a raw deflate compressor with an 8 bit window, so
+        # 8 is unusable for the window we compress with, even though it is a
+        # legal value on the wire and fine for the window we decompress with.
+        # RFC 7692 7.1.2.1 lets a server decline an offer it cannot support.
+        if server_max_window_bits == 8:
+            raise NegotiationError("unsupported server_max_window_bits")
+
         return (
             _build_parameters(
                 server_no_context_takeover,
diff --git a/tests/extensions/test_permessage_deflate.py b/tests/extensions/test_permessage_deflate.py
index 71f8e8e4..bdb88113 100644
--- a/tests/extensions/test_permessage_deflate.py
+++ b/tests/extensions/test_permessage_deflate.py
@@ -463,6 +463,12 @@ def test_process_response_params(self):
                 [("server_max_window_bits", "7")],
                 NegotiationError,
             ),
+            (
+                # 8 is legal for the window we decompress with.
+                (False, False, None, None),
+                [("server_max_window_bits", "8")],
+                (False, False, 8, 15),
+            ),
             (
                 (False, False, None, None),
                 [("server_max_window_bits", "10")],
@@ -519,6 +525,12 @@ def test_process_response_params(self):
                 [("client_max_window_bits", "7")],
                 NegotiationError,
             ),
+            (
+                # 8 is unusable for the window we compress with.
+                (False, False, None, True),
+                [("client_max_window_bits", "8")],
+                NegotiationError,
+            ),
             (
                 (False, False, None, True),
                 [("client_max_window_bits", "10")],
@@ -774,6 +786,14 @@ def test_process_request_params(self):
                 None,
                 NegotiationError,
             ),
+            (
+                # 8 is unusable for the window we compress with; RFC 7692
+                # 7.1.2.1 lets the server decline the offer.
+                (False, False, None, None),
+                [("server_max_window_bits", "8")],
+                None,
+                NegotiationError,
+            ),
             (
                 (False, False, None, None),
                 [("server_max_window_bits", "10")],
@@ -835,6 +855,13 @@ def test_process_request_params(self):
                 None,
                 InvalidParameterValue,
             ),
+            (
+                # 8 is legal for the window we decompress with.
+                (False, False, None, None),
+                [("client_max_window_bits", "8")],
+                [("client_max_window_bits", "8")],  # doesn't matter
+                (False, False, 8, 15),
+            ),
             (
                 (False, False, None, None),
                 [("client_max_window_bits", "10")],