diff --git a/src/mcp/client/stdio.py b/src/mcp/client/stdio.py
index 902dc8576..110d0d353 100644
--- a/src/mcp/client/stdio.py
+++ b/src/mcp/client/stdio.py
@@ -205,6 +205,12 @@ async def stdin_writer():
             except ProcessLookupError:  # pragma: no cover
                 # Process already exited, which is fine
                 pass
+
+            if process.stdout:  # pragma: no branch
+                try:
+                    await process.stdout.aclose()
+                except Exception:  # pragma: no cover
+                    pass
             await read_stream.aclose()
             await write_stream.aclose()
             await read_stream_writer.aclose()
diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index 9cdf717c7..cb82ba3ae 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -10,7 +10,7 @@
 
 import anyio
 import httpx
-from anyio.abc import TaskGroup
+from anyio.abc import TaskGroup, TaskStatus
 from httpx_sse import EventSource, ServerSentEvent, aconnect_sse
 from pydantic import ValidationError
 
@@ -437,10 +437,13 @@ async def post_writer(
         write_stream: ContextSendStream[SessionMessage],
         start_get_stream: Callable[[], None],
         tg: TaskGroup,
+        *,
+        task_status: TaskStatus[None] = anyio.TASK_STATUS_IGNORED,
     ) -> None:
         """Handle writing requests to the server."""
         try:
             async with write_stream_reader, read_stream_writer, write_stream:
+                task_status.started(None)
 
                 async def _handle_message(session_message: SessionMessage) -> None:
                     message = session_message.message
@@ -570,7 +573,7 @@ async def streamable_http_client(
             def start_get_stream() -> None:
                 tg.start_soon(transport.handle_get_stream, client, read_stream_writer)
 
-            tg.start_soon(
+            await tg.start(
                 transport.post_writer,
                 client,
                 write_stream_reader,
diff --git a/tests/shared/test_streamable_http.py b/tests/shared/test_streamable_http.py
index b43a3361c..346fd5f81 100644
--- a/tests/shared/test_streamable_http.py
+++ b/tests/shared/test_streamable_http.py
@@ -868,6 +868,46 @@ async def test_streamable_http_client_basic_connection(basic_app: Starlette) ->
         assert result.server_info.name == SERVER_NAME
 
 
+@pytest.mark.anyio
+async def test_streamable_http_client_no_race_on_consecutive_requests(basic_app: Starlette) -> None:
+    """The first request after initialize can run repeatedly without racing startup."""
+    for iteration in range(10):  # pragma: no branch
+        async with (
+            make_client(basic_app) as http_client,
+            streamable_http_client(f"{BASE_URL}/mcp", http_client=http_client) as (read_stream, write_stream),
+            ClientSession(read_stream, write_stream) as session,
+        ):
+            await session.initialize()
+
+            tools = await session.list_tools()
+            assert len(tools.tools) == 8, f"Iteration {iteration}: expected 8 tools, got {len(tools.tools)}"
+            assert tools.tools[0].name == "test_tool"
+
+            tools2 = await session.list_tools()
+            assert len(tools2.tools) == 8
+
+            resource = await session.read_resource(uri="foobar://test-iteration")
+            assert len(resource.contents) == 1
+
+
+@pytest.mark.anyio
+async def test_streamable_http_client_rapid_request_sequence(basic_app: Starlette) -> None:
+    """A rapid sequence of requests reuses the initialized stream reliably."""
+    async with (
+        make_client(basic_app) as http_client,
+        streamable_http_client(f"{BASE_URL}/mcp", http_client=http_client) as (read_stream, write_stream),
+        ClientSession(read_stream, write_stream) as session,
+    ):
+        await session.initialize()
+
+        for i in range(20):
+            tools = await session.list_tools()
+            assert len(tools.tools) == 8, f"Request {i}: expected 8 tools, got {len(tools.tools)}"
+
+        resource = await session.read_resource(uri="foobar://final-test")
+        assert len(resource.contents) == 1
+
+
 @pytest.mark.anyio
 async def test_streamable_http_client_resource_read(initialized_client_session: ClientSession) -> None:
     """A resource read round-trips its arguments and the handler's content."""