diff --git a/kafka/conn.py b/kafka/conn.py
index 31e1f8be9..8dd65c1c0 100644
--- a/kafka/conn.py
+++ b/kafka/conn.py
@@ -301,6 +301,7 @@ def __init__(self, host, port, afi, **configs):
         if self.config['ssl_context'] is not None:
             self._ssl_context = self.config['ssl_context']
         self._api_versions_future = None
+        self._api_versions_check_timeout = self.config['api_version_auto_timeout_ms']
         self._sasl_auth_future = None
         self.last_attempt = 0
         self._gai = []
@@ -557,7 +558,8 @@ def _try_api_versions_check(self):
                 else:
                     request = ApiVersionsRequest[version]()
                 future = Future()
-                response = self._send(request, blocking=True, request_timeout_ms=(self.config['api_version_auto_timeout_ms'] * 0.8))
+                self._api_versions_check_timeout /= 2
+                response = self._send(request, blocking=True, request_timeout_ms=self._api_versions_check_timeout)
                 response.add_callback(self._handle_api_versions_response, future)
                 response.add_errback(self._handle_api_versions_failure, future)
                 self._api_versions_future = future
@@ -566,7 +568,8 @@ def _try_api_versions_check(self):
             elif self._check_version_idx < len(self.VERSION_CHECKS):
                 version, request = self.VERSION_CHECKS[self._check_version_idx]
                 future = Future()
-                response = self._send(request, blocking=True, request_timeout_ms=(self.config['api_version_auto_timeout_ms'] * 0.8))
+                self._api_versions_check_timeout /= 2
+                response = self._send(request, blocking=True, request_timeout_ms=self._api_versions_check_timeout)
                 response.add_callback(self._handle_check_version_response, future, version)
                 response.add_errback(self._handle_check_version_failure, future)
                 self._api_versions_future = future
@@ -618,7 +621,13 @@ def _handle_api_versions_response(self, future, response):
 
     def _handle_api_versions_failure(self, future, ex):
         future.failure(ex)
-        self._check_version_idx = 0
+        # Modern brokers should not disconnect on unrecognized api-versions request,
+        # but in case they do we always want to try v0 as a fallback
+        # otherwise switch to check_version probe.
+        if self._api_versions_idx > 0:
+            self._api_versions_idx = 0
+        else:
+            self._check_version_idx = 0
         # after failure connection is closed, so state should already be DISCONNECTED
 
     def _handle_check_version_response(self, future, version, _response):