diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 879d6fd788d..2f2e739f77c 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -306,7 +306,7 @@ class BasicSocketTests(unittest.TestCase):
         self.assertGreaterEqual(fix, 0)
         self.assertLess(fix, 256)
         self.assertGreaterEqual(patch, 0)
-        self.assertLessEqual(patch, 26)
+        self.assertLessEqual(patch, 63)
         self.assertGreaterEqual(status, 0)
         self.assertLessEqual(status, 15)
         # Version string as returned by {Open,Libre}SSL, the format might change
diff --git a/Misc/NEWS b/Misc/NEWS
index 4fcee12d008..e23ad9076f2 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -1727,6 +1727,9 @@ Tests
 
 - Issue #23211: Workaround test_logging failure on some OS X 10.6 systems.
 
+- Issue #23345: Prevent test_ssl failures with large OpenSSL patch level
+  values (like 0.9.8zc).
+
 Tools/Demos
 -----------