diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index 9a971704e4..af0f88c219 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -1639,6 +1639,27 @@ object object_api<Derived>::call(Args &&...args) const {
     return operator()<policy>(std::forward<Args>(args)...);
 }
 
+// Convert list -> tuple and set -> frozenset for use as keys in dict, set etc.
+// https://mail.python.org/pipermail/python-dev/2005-October/057586.html
+inline object freeze(object &&obj) {
+    if (isinstance<list>(obj)) {
+        return tuple(std::move(obj));
+    }
+    if (isinstance<set>(obj)) {
+        return frozenset(std::move(obj));
+    }
+    return std::move(obj);
+}
+
+template <typename Caster, typename SFINAE = void>
+struct frozen_type_name {
+    static constexpr auto name = Caster::name;
+};
+template <typename Caster>
+struct frozen_type_name<Caster, void_t<decltype(Caster::frozen_name)>> {
+    static constexpr auto name = Caster::frozen_name;
+};
+
 PYBIND11_NAMESPACE_END(detail)
 
 template <typename T>
diff --git a/include/pybind11/stl.h b/include/pybind11/stl.h
index 597bce61d5..9b5a6bf5d5 100644
--- a/include/pybind11/stl.h
+++ b/include/pybind11/stl.h
@@ -79,14 +79,17 @@ struct set_caster {
         for (auto &&value : src) {
             auto value_ = reinterpret_steal<object>(
                 key_conv::cast(forward_like<T>(value), policy, parent));
-            if (!value_ || !s.add(std::move(value_))) {
+            if (!value_ || !s.add(freeze(std::move(value_)))) {
                 return handle();
             }
         }
         return s.release();
     }
 
-    PYBIND11_TYPE_CASTER(type, const_name("Set[") + key_conv::name + const_name("]"));
+    PYBIND11_TYPE_CASTER(type,
+                         const_name("Set[") + frozen_type_name<key_conv>::name + const_name("]"));
+    static constexpr auto frozen_name
+        = const_name("FrozenSet[") + frozen_type_name<key_conv>::name + const_name("]");
 };
 
 template <typename Type, typename Key, typename Value>
@@ -128,14 +131,14 @@ struct map_caster {
             if (!key || !value) {
                 return handle();
             }
-            d[key] = value;
+            d[freeze(std::move(key))] = std::move(value);
         }
         return d.release();
     }
 
     PYBIND11_TYPE_CASTER(Type,
-                         const_name("Dict[") + key_conv::name + const_name(", ") + value_conv::name
-                             + const_name("]"));
+                         const_name("Dict[") + frozen_type_name<key_conv>::name + const_name(", ")
+                             + value_conv::name + const_name("]"));
 };
 
 template <typename Type, typename Value>
@@ -188,6 +191,8 @@ struct list_caster {
     }
 
     PYBIND11_TYPE_CASTER(Type, const_name("List[") + value_conv::name + const_name("]"));
+    static constexpr auto frozen_name
+        = const_name("Tuple[") + value_conv::name + const_name(", ...]");
 };
 
 template <typename Type, typename Alloc>
@@ -257,6 +262,11 @@ struct array_caster {
                                                      const_name("[") + const_name<Size>()
                                                          + const_name("]"))
                              + const_name("]"));
+    static constexpr auto frozen_name
+        = const_name("Tuple[") + value_conv::name
+          + const_name<Resizable>(const_name(", ..."),
+                                  const_name("[") + const_name<Size>() + const_name("]"))
+          + const_name("]");
 };
 
 template <typename Type, size_t Size>
diff --git a/tests/test_stl.cpp b/tests/test_stl.cpp
index 38d32fda93..5c51db9b52 100644
--- a/tests/test_stl.cpp
+++ b/tests/test_stl.cpp
@@ -249,6 +249,22 @@ TEST_SUBMODULE(stl, m) {
         return v;
     });
 
+    // test_frozen_key
+    m.def("cast_set_map", []() {
+        return std::map<std::set<std::string>, std::string>{{{"key1", "key2"}, "value"}};
+    });
+    m.def("load_set_map", [](const std::map<std::set<std::string>, std::string> &map) {
+        return map.at({"key1", "key2"}) == "value" && map.at({"key3"}) == "value2";
+    });
+    m.def("cast_set_set", []() { return std::set<std::set<std::string>>{{"key1", "key2"}}; });
+    m.def("load_set_set", [](const std::set<std::set<std::string>> &set) {
+        return (set.count({"key1", "key2"}) != 0u) && (set.count({"key3"}) != 0u);
+    });
+    m.def("cast_vector_set", []() { return std::set<std::vector<int>>{{1, 2}}; });
+    m.def("load_vector_set", [](const std::set<std::vector<int>> &set) {
+        return (set.count({1, 2}) != 0u) && (set.count({3}) != 0u);
+    });
+
     pybind11::enum_<EnumType>(m, "EnumType")
         .value("kSet", EnumType::kSet)
         .value("kUnset", EnumType::kUnset);
diff --git a/tests/test_stl.py b/tests/test_stl.py
index d30c382113..11a445019b 100644
--- a/tests/test_stl.py
+++ b/tests/test_stl.py
@@ -98,6 +98,38 @@ def test_recursive_casting():
     assert z[0].value == 7 and z[1].value == 42
 
 
+def test_frozen_key(doc):
+    """Test that we special-case C++ key types to Python immutable containers, e.g.:
+    std::map<std::set<K>, V> <-> dict[frozenset[K], V]
+    std::set<std::set<T>> <-> set[frozenset[T]]
+    std::set<std::vector<T>> <-> set[tuple[T, ...]]
+    """
+    s = m.cast_set_map()
+    assert s == {frozenset({"key1", "key2"}): "value"}
+    s[frozenset({"key3"})] = "value2"
+    assert m.load_set_map(s)
+    assert doc(m.cast_set_map) == "cast_set_map() -> Dict[FrozenSet[str], str]"
+    assert (
+        doc(m.load_set_map) == "load_set_map(arg0: Dict[FrozenSet[str], str]) -> bool"
+    )
+
+    s = m.cast_set_set()
+    assert s == {frozenset({"key1", "key2"})}
+    s.add(frozenset({"key3"}))
+    assert m.load_set_set(s)
+    assert doc(m.cast_set_set) == "cast_set_set() -> Set[FrozenSet[str]]"
+    assert doc(m.load_set_set) == "load_set_set(arg0: Set[FrozenSet[str]]) -> bool"
+
+    s = m.cast_vector_set()
+    assert s == {(1, 2)}
+    s.add((3,))
+    assert m.load_vector_set(s)
+    assert doc(m.cast_vector_set) == "cast_vector_set() -> Set[Tuple[int, ...]]"
+    assert (
+        doc(m.load_vector_set) == "load_vector_set(arg0: Set[Tuple[int, ...]]) -> bool"
+    )
+
+
 def test_move_out_container():
     """Properties use the `reference_internal` policy by default. If the underlying function
     returns an rvalue, the policy is automatically changed to `move` to avoid referencing