diff --git a/tests/test_pickling.cpp b/tests/test_pickling.cpp
index 9787bd300..e154bc483 100644
--- a/tests/test_pickling.cpp
+++ b/tests/test_pickling.cpp
@@ -61,6 +61,8 @@ void wrap(py::module m) {
 } // namespace exercise_trampoline
 
 TEST_SUBMODULE(pickling, m) {
+    m.def("simple_callable", []() { return 20220426; });
+
     // test_roundtrip
     class Pickleable {
     public:
diff --git a/tests/test_pickling.py b/tests/test_pickling.py
index 52802ace8..12361a661 100644
--- a/tests/test_pickling.py
+++ b/tests/test_pickling.py
@@ -1,4 +1,5 @@
 import pickle
+import re
 
 import pytest
 
@@ -6,6 +7,20 @@ import env
 from pybind11_tests import pickling as m
 
 
+def test_pickle_simple_callable():
+    assert m.simple_callable() == 20220426
+    if env.PYPY:
+        serialized = pickle.dumps(m.simple_callable)
+        deserialized = pickle.loads(serialized)
+        assert deserialized() == 20220426
+    else:
+        # To document broken behavior: currently it fails universally with
+        # all C Python versions.
+        with pytest.raises(TypeError) as excinfo:
+            pickle.dumps(m.simple_callable)
+        assert re.search("can.*t pickle .*PyCapsule.* object", str(excinfo.value))
+
+
 @pytest.mark.parametrize("cls_name", ["Pickleable", "PickleableNew"])
 def test_roundtrip(cls_name):
     cls = getattr(m, cls_name)