diff --git a/src/websockets/asyncio/server.py b/src/websockets/asyncio/server.py
index ef9bd807..0766ee0b 100644
--- a/src/websockets/asyncio/server.py
+++ b/src/websockets/asyncio/server.py
@@ -11,7 +11,7 @@
 from types import TracebackType
 from typing import Any, Callable, Mapping, cast
 
-from ..exceptions import InvalidHeader
+from ..exceptions import InvalidHandshake, InvalidHeader, InvalidMessage
 from ..extensions.base import ServerExtensionFactory
 from ..extensions.permessage_deflate import enable_server_permessage_deflate
 from ..frames import CloseCode
@@ -204,7 +204,13 @@ async def handshake(
         # response that rejects the handshake.
 
         if self.protocol.handshake_exc is not None:
-            raise self.protocol.handshake_exc
+            # Suppress re-raise for unsupported HTTP methods (HEAD, POST, etc.)
+            # — the connection is already being closed cleanly by send_eof().
+            if not (
+                isinstance(self.protocol.handshake_exc, InvalidMessage)
+                and isinstance(self.protocol.handshake_exc.__cause__, InvalidHandshake)
+            ):
+                raise self.protocol.handshake_exc
 
     def process_event(self, event: Event) -> None:
         """
diff --git a/src/websockets/http11.py b/src/websockets/http11.py
index 230e5015..422ccd64 100644
--- a/src/websockets/http11.py
+++ b/src/websockets/http11.py
@@ -9,7 +9,7 @@
 from typing import Callable
 
 from .datastructures import Headers
-from .exceptions import SecurityError
+from .exceptions import InvalidHandshake, SecurityError
 from .version import version as websockets_version
 
 
@@ -148,7 +148,9 @@ def parse(
                 f"unsupported protocol; expected HTTP/1.1: {d(request_line)}"
             )
         if method != b"GET":
-            raise ValueError(f"unsupported HTTP method; expected GET; got {d(method)}")
+            raise InvalidHandshake(
+                f"unsupported HTTP method; expected GET; got {d(method)}"
+            )
 
         # RFC 9110 defers the definition of URIs to RFC 3986, which allows only
         # a subset of ASCII. Non-ASCII IRIs must be UTF-8 then percent-encoded.
diff --git a/src/websockets/server.py b/src/websockets/server.py
index de2c6354..5dbd09de 100644
--- a/src/websockets/server.py
+++ b/src/websockets/server.py
@@ -552,6 +552,18 @@ def parse(self) -> Generator[None]:
                     "did not receive a valid HTTP request"
                 )
                 self.handshake_exc.__cause__ = exc
+                if isinstance(exc, InvalidHandshake):
+                    # Send HTTP 405 for unsupported methods — matching
+                    # gorilla/websocket (StatusMethodNotAllowed) and ws
+                    # (405 abortHandshake).  send_response() already
+                    # closes the connection for non-101 responses, so
+                    # skip the common handler below.
+                    response = self.reject(
+                        405, "Only GET is supported.\n"
+                    )
+                    self.send_response(response)
+                    yield
+                    return
                 self.send_eof()
                 self.parser = self.discard()
                 next(self.parser)  # start coroutine
diff --git a/src/websockets/sync/server.py b/src/websockets/sync/server.py
index ffd82fba..a345358b 100644
--- a/src/websockets/sync/server.py
+++ b/src/websockets/sync/server.py
@@ -15,7 +15,7 @@
 from types import TracebackType
 from typing import Any, Callable, Mapping, cast
 
-from ..exceptions import InvalidHeader
+from ..exceptions import InvalidHandshake, InvalidHeader, InvalidMessage
 from ..extensions.base import ServerExtensionFactory
 from ..extensions.permessage_deflate import enable_server_permessage_deflate
 from ..frames import CloseCode
@@ -186,7 +186,13 @@ def handshake(
         # response that rejects the handshake.
 
         if self.protocol.handshake_exc is not None:
-            raise self.protocol.handshake_exc
+            # Suppress re-raise for unsupported HTTP methods (HEAD, POST, etc.)
+            # — the connection is already being closed cleanly by send_eof().
+            if not (
+                isinstance(self.protocol.handshake_exc, InvalidMessage)
+                and isinstance(self.protocol.handshake_exc.__cause__, InvalidHandshake)
+            ):
+                raise self.protocol.handshake_exc
 
     def process_event(self, event: Event) -> None:
         """
diff --git a/tests/test_http11.py b/tests/test_http11.py
index fb6fca34..8ba478c6 100644
--- a/tests/test_http11.py
+++ b/tests/test_http11.py
@@ -1,5 +1,5 @@
 from websockets.datastructures import Headers
-from websockets.exceptions import SecurityError
+from websockets.exceptions import InvalidHandshake, SecurityError
 from websockets.http11 import *
 from websockets.http11 import parse_headers
 from websockets.streams import StreamReader
@@ -61,7 +61,7 @@ def test_parse_unsupported_protocol(self):
 
     def test_parse_unsupported_method(self):
         self.reader.feed_data(b"OPTIONS * HTTP/1.1\r\n\r\n")
-        with self.assertRaises(ValueError) as raised:
+        with self.assertRaises(InvalidHandshake) as raised:
             next(self.parse())
         self.assertEqual(
             str(raised.exception),