diff --git a/src/finch/_streaming.py b/src/finch/_streaming.py
index b0600fc9..913159fd 100644
--- a/src/finch/_streaming.py
+++ b/src/finch/_streaming.py
@@ -45,10 +45,15 @@ def __stream__(self) -> Iterator[ResponseT]:
         cast_to = self._cast_to
         response = self.response
         process_data = self._client._process_response_data
+        iterator = self._iter_events()
 
-        for sse in self._iter_events():
+        for sse in iterator:
             yield process_data(data=sse.json(), cast_to=cast_to, response=response)
 
+        # Ensure the entire stream is consumed
+        for sse in iterator:
+            ...
+
 
 class AsyncStream(Generic[ResponseT]):
     """Provides the core interface to iterate over an asynchronous stream response."""
@@ -83,10 +88,15 @@ async def __stream__(self) -> AsyncIterator[ResponseT]:
         cast_to = self._cast_to
         response = self.response
         process_data = self._client._process_response_data
+        iterator = self._iter_events()
 
-        async for sse in self._iter_events():
+        async for sse in iterator:
             yield process_data(data=sse.json(), cast_to=cast_to, response=response)
 
+        # Ensure the entire stream is consumed
+        async for sse in iterator:
+            ...
+
 
 class ServerSentEvent:
     def __init__(