diff --git a/docs/advanced/functions.rst b/docs/advanced/functions.rst
index 6a93ab9da..f6061ffbe 100644
--- a/docs/advanced/functions.rst
+++ b/docs/advanced/functions.rst
@@ -182,6 +182,9 @@ relies on the ability to create a *weak reference* to the nurse object. When
 the nurse object is not a pybind11-registered type and does not support weak
 references, an exception will be thrown.
 
+If you use an incorrect argument index, you will get a ``RuntimeError`` saying
+``Could not activate keep_alive!``. You should review the indices you're using.
+
 Consider the following example: here, the binding code for a list append
 operation ties the lifetime of the newly added element to the underlying
 container:
diff --git a/tests/test_call_policies.cpp b/tests/test_call_policies.cpp
index 26c83f81b..7cb98d0d8 100644
--- a/tests/test_call_policies.cpp
+++ b/tests/test_call_policies.cpp
@@ -51,6 +51,7 @@ TEST_SUBMODULE(call_policies, m) {
         void addChild(Child *) { }
         Child *returnChild() { return new Child(); }
         Child *returnNullChild() { return nullptr; }
+        static Child *staticFunction(Parent*) { return new Child(); }
     };
     py::class_<Parent>(m, "Parent")
         .def(py::init<>())
@@ -60,7 +61,12 @@ TEST_SUBMODULE(call_policies, m) {
         .def("returnChild", &Parent::returnChild)
         .def("returnChildKeepAlive", &Parent::returnChild, py::keep_alive<1, 0>())
         .def("returnNullChildKeepAliveChild", &Parent::returnNullChild, py::keep_alive<1, 0>())
-        .def("returnNullChildKeepAliveParent", &Parent::returnNullChild, py::keep_alive<0, 1>());
+        .def("returnNullChildKeepAliveParent", &Parent::returnNullChild, py::keep_alive<0, 1>())
+        .def_static(
+            "staticFunction", &Parent::staticFunction, py::keep_alive<1, 0>());
+
+    m.def("free_function", [](Parent*, Child*) {}, py::keep_alive<1, 2>());
+    m.def("invalid_arg_index", []{}, py::keep_alive<0, 1>());
 
 #if !defined(PYPY_VERSION)
     // test_alive_gc
diff --git a/tests/test_call_policies.py b/tests/test_call_policies.py
index e0413d145..af017e9d0 100644
--- a/tests/test_call_policies.py
+++ b/tests/test_call_policies.py
@@ -46,6 +46,19 @@ def test_keep_alive_argument(capture):
     """
     )
 
+    p = m.Parent()
+    c = m.Child()
+    assert ConstructorStats.detail_reg_inst() == n_inst + 2
+    m.free_function(p, c)
+    del c
+    assert ConstructorStats.detail_reg_inst() == n_inst + 2
+    del p
+    assert ConstructorStats.detail_reg_inst() == n_inst
+
+    with pytest.raises(RuntimeError) as excinfo:
+        m.invalid_arg_index()
+    assert str(excinfo.value) == "Could not activate keep_alive!"
+
 
 def test_keep_alive_return_value(capture):
     n_inst = ConstructorStats.detail_reg_inst()
@@ -85,6 +98,23 @@ def test_keep_alive_return_value(capture):
     """
     )
 
+    p = m.Parent()
+    assert ConstructorStats.detail_reg_inst() == n_inst + 1
+    with capture:
+        m.Parent.staticFunction(p)
+        assert ConstructorStats.detail_reg_inst() == n_inst + 2
+    assert capture == "Allocating child."
+    with capture:
+        del p
+        assert ConstructorStats.detail_reg_inst() == n_inst
+    assert (
+        capture
+        == """
+        Releasing parent.
+        Releasing child.
+    """
+    )
+
 
 # https://foss.heptapod.net/pypy/pypy/-/issues/2447
 @pytest.mark.xfail("env.PYPY", reason="_PyObject_GetDictPtr is unimplemented")