diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 6c342d8..e9e80ee 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -275,7 +275,7 @@
         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 494a386..433ce0d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -92,6 +92,9 @@
 - Issue #18905: "pydoc -p 0" now outputs actually used port.  Based on patch by
   Wieland Hoffmann.
 
+- Issue #23345: Prevent test_ssl failures with large OpenSSL patch level
+  values (like 0.9.8zc).
+
 Tests
 -----