diff --git a/httpx/_transports/wsgi.py b/httpx/_transports/wsgi.py
index 58e8309d..e71f1604 100644
--- a/httpx/_transports/wsgi.py
+++ b/httpx/_transports/wsgi.py
@@ -16,12 +16,17 @@ def _skip_leading_empty_chunks(body: typing.Iterable) -> typing.Iterable:
 
 class WSGIByteStream(SyncByteStream):
     def __init__(self, result: typing.Iterable[bytes]) -> None:
+        self._close = getattr(result, "close", None)
         self._result = _skip_leading_empty_chunks(result)
 
     def __iter__(self) -> typing.Iterator[bytes]:
         for part in self._result:
             yield part
 
+    def close(self) -> None:
+        if self._close is not None:
+            self._close()
+
 
 class WSGITransport(BaseTransport):
     """
diff --git a/tests/test_wsgi.py b/tests/test_wsgi.py
index b130e53c..164899b5 100644
--- a/tests/test_wsgi.py
+++ b/tests/test_wsgi.py
@@ -1,4 +1,5 @@
 import sys
+import wsgiref.validate
 from functools import partial
 
 import pytest
@@ -19,7 +20,7 @@ def application_factory(output):
         for item in output:
             yield item
 
-    return application
+    return wsgiref.validate.validator(application)
 
 
 def echo_body(environ, start_response):