diff --git a/Lib/test/test_sets.py b/Lib/test/test_sets.py
index a2aa69a45f0..b56219be244 100644
--- a/Lib/test/test_sets.py
+++ b/Lib/test/test_sets.py
@@ -138,6 +138,10 @@ class TestSetOfSets(unittest.TestCase):
         outer = Set([inner])
         element = outer.pop()
         assert type(element) == ImmutableSet, "Construct set of sets"
+        outer.add(inner)        # Rebuild set of sets with .add method
+        outer.remove(inner)
+        assert outer == Set()   # Verify that remove worked
+        outer.discard(inner)    # Absence of KeyError indicates working fine
 
 #==============================================================================