diff --git a/src/replit_river/client_transport.py b/src/replit_river/client_transport.py
index 1e8fdcf1..cd3be09d 100644
--- a/src/replit_river/client_transport.py
+++ b/src/replit_river/client_transport.py
@@ -170,7 +170,7 @@ async def _establish_new_connection(
 
             try:
                 uri_and_metadata = await self._uri_and_metadata_factory()
-                ws = await websockets.connect(uri_and_metadata["uri"])
+                ws = await websockets.connect(uri_and_metadata["uri"], max_size=None)
                 session_id = (
                     self.generate_nanoid()
                     if not old_session
diff --git a/src/replit_river/v2/session.py b/src/replit_river/v2/session.py
index 99b30e82..9600f4cc 100644
--- a/src/replit_river/v2/session.py
+++ b/src/replit_river/v2/session.py
@@ -1084,7 +1084,10 @@ async def _do_ensure_connected[HandshakeMetadata](
         ws: ClientConnection | None = None
         try:
             uri_and_metadata = await uri_and_metadata_factory()
-            ws = await websockets.asyncio.client.connect(uri_and_metadata["uri"])
+            ws = await websockets.asyncio.client.connect(
+                uri_and_metadata["uri"],
+                max_size=None,
+            )
             transition_connecting(ws)
 
             try:
diff --git a/tests/v2/test_v2_session_lifecycle.py b/tests/v2/test_v2_session_lifecycle.py
index 2fa8d0e2..bea6d2e0 100644
--- a/tests/v2/test_v2_session_lifecycle.py
+++ b/tests/v2/test_v2_session_lifecycle.py
@@ -1,17 +1,26 @@
 import asyncio
+import logging
 from typing import AsyncIterator, Awaitable, Callable, TypeAlias, TypedDict
 
+import msgpack
+import nanoid
 import pytest
-from websockets import ConnectionClosedOK
+from websockets import ConnectionClosed, ConnectionClosedOK
 from websockets.asyncio.server import ServerConnection, serve
 from websockets.typing import Data
 
 from replit_river.common_session import SessionState
 from replit_river.messages import parse_transport_msg
 from replit_river.rate_limiter import RateLimiter
-from replit_river.rpc import TransportMessage
+from replit_river.rpc import (
+    ControlMessageHandshakeRequest,
+    ControlMessageHandshakeResponse,
+    HandShakeStatus,
+    TransportMessage,
+)
 from replit_river.transport_options import TransportOptions, UriAndMetadata
-from replit_river.v2.session import Session
+from replit_river.v2.client import Client
+from replit_river.v2.session import STREAM_CLOSED_BIT, Session
 
 
 class _PermissiveRateLimiter(RateLimiter):
@@ -54,6 +63,8 @@ async def handle(websocket: ServerConnection) -> None:
                 await recv.put(datagram)
         except ConnectionClosedOK:
             pass
+        except ConnectionClosed:
+            pass
 
     port: int | None = None
     if state["ipv4_laddr"]:
@@ -65,7 +76,10 @@ async def handle(websocket: ServerConnection) -> None:
                     state["ipv4_laddr"] = pair
         serve_forever = asyncio.create_task(server.serve_forever())
         yield None
-        serve_forever.cancel()
+        server.close()
+        await server.wait_closed()
+        # "serve_forever" should always be done after wait_closed finishes
+        assert serve_forever.done()
 
 
 @pytest.fixture
@@ -145,3 +159,89 @@ def close_session_callback(_session: Session) -> None:
     await connecting
     assert session._state == SessionState.CLOSED
     assert callcount == 1
+
+
+async def test_big_packet(ws_server: WsServerFixture) -> None:
+    (urimeta, recv, conn) = ws_server
+
+    client = Client(
+        client_id="CLIENT1",
+        server_id="SERVER",
+        transport_options=TransportOptions(),
+        uri_and_metadata_factory=urimeta,
+    )
+
+    connecting = asyncio.create_task(client.ensure_connected())
+    request_msg = parse_transport_msg(await recv.get())
+
+    assert not isinstance(request_msg, str)
+    assert (serverconn := conn())
+    handshake_request: ControlMessageHandshakeRequest[None] = (
+        ControlMessageHandshakeRequest(**request_msg.payload)
+    )
+
+    handshake_resp = ControlMessageHandshakeResponse(
+        status=HandShakeStatus(
+            ok=True,
+        ),
+    )
+    handshake_request.sessionId
+
+    msg = TransportMessage(
+        from_=request_msg.from_,
+        to=request_msg.to,
+        streamId=request_msg.streamId,
+        controlFlags=0,
+        id=nanoid.generate(),
+        seq=0,
+        ack=0,
+        payload=handshake_resp.model_dump(),
+    )
+    packed = msgpack.packb(
+        msg.model_dump(by_alias=True, exclude_none=True), datetime=True
+    )
+    await serverconn.send(packed)
+
+    async def handle_server_messages() -> None:
+        request_msg = parse_transport_msg(await recv.get())
+        assert not isinstance(request_msg, str)
+        msg = TransportMessage(
+            from_=request_msg.to,
+            to=request_msg.from_,
+            streamId=request_msg.streamId,
+            controlFlags=STREAM_CLOSED_BIT,
+            id=nanoid.generate(),
+            seq=0,
+            ack=0,
+            payload={
+                "ok": True,
+                "payload": {
+                    "big": "a" * (2**20 + 1),  # One more than the default max_size
+                },
+            },
+        )
+
+        packed = msgpack.packb(
+            msg.model_dump(by_alias=True, exclude_none=True), datetime=True
+        )
+        await serverconn.send(packed)
+
+        stream_close_msg = msgpack.unpackb(await recv.get())
+        assert stream_close_msg["controlFlags"] == STREAM_CLOSED_BIT
+
+    stream_handler = asyncio.create_task(handle_server_messages())
+
+    try:
+        async for datagram in client.send_subscription(
+            "test", "bigstream", {}, lambda x: x, lambda x: x, lambda x: x
+        ):
+            print(datagram)
+    except Exception:
+        logging.exception("Interrupted")
+
+    await client.close()
+    await connecting
+
+    # Ensure we're listening to close messages as well
+    stream_handler.cancel()
+    await stream_handler