diff --git a/Lib/CGIHTTPServer.py b/Lib/CGIHTTPServer.py
index ed37348..13ca0b5 100644
--- a/Lib/CGIHTTPServer.py
+++ b/Lib/CGIHTTPServer.py
@@ -289,6 +289,8 @@
             self.wfile.write(stdout)
             if stderr:
                 self.log_error('%s', stderr)
+            p.stderr.close()
+            p.stdout.close()
             status = p.returncode
             if status:
                 self.log_error("CGI script exit status %#x", status)