diff --git a/Lib/test/test_ucn.py b/Lib/test/test_ucn.py
index 775044b..1d303dc 100644
--- a/Lib/test/test_ucn.py
+++ b/Lib/test/test_ucn.py
@@ -8,6 +8,7 @@
 """#"
 
 import unittest
+import _testcapi
 
 from test import test_support
 
@@ -137,6 +138,21 @@
             unicode, "\\NSPACE", 'unicode-escape', 'strict'
         )
 
+    @unittest.skipUnless(_testcapi.INT_MAX < _testcapi.PY_SSIZE_T_MAX,
+                         "needs UINT_MAX < SIZE_MAX")
+    def test_issue16335(self):
+        # very very long bogus character name
+        try:
+            x = b'\\N{SPACE' + b'x' * int(_testcapi.UINT_MAX + 1) + b'}'
+        except MemoryError:
+            raise unittest.SkipTest("not enough memory")
+        self.assertEqual(len(x), len(b'\\N{SPACE}') + (_testcapi.UINT_MAX + 1))
+        self.assertRaisesRegex(UnicodeError,
+            'unknown Unicode character name',
+            x.decode, 'unicode-escape'
+        )
+
+
 def test_main():
     test_support.run_unittest(UnicodeNamesTest)