diff --git a/Lib/test/test_asyncio/test_sslproto.py b/Lib/test/test_asyncio/test_sslproto.py
index 5c861e92b7d..4645cc044a5 100644
--- a/Lib/test/test_asyncio/test_sslproto.py
+++ b/Lib/test/test_asyncio/test_sslproto.py
@@ -498,6 +498,12 @@ class BaseStartTLS(func_tests.FunctionalTestCaseMixin):
 
         server_context = test_utils.simple_server_sslcontext()
         client_context = test_utils.simple_client_sslcontext()
+        if sys.platform.startswith('freebsd') or sys.platform.startswith('win'):
+            # bpo-35031: Some FreeBSD and Windows buildbots fail to run this test
+            # as the eof was not being received by the server if the payload
+            # size is not big enough. This behaviour only appears if the
+            # client is using TLS1.3.
+            client_context.options |= ssl.OP_NO_TLSv1_3
         answer = None
 
         def client(sock, addr):