diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index be206e1a6..cfa442067 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -2069,12 +2069,12 @@ struct enum_base {
         str name(name_);
         if (entries.contains(name)) {
             std::string type_name = (std::string) str(m_base.attr("__name__"));
-            throw value_error(type_name + ": element \"" + std::string(name_)
+            throw value_error(std::move(type_name) + ": element \"" + std::string(name_)
                               + "\" already exists!");
         }
 
         entries[name] = std::make_pair(value, doc);
-        m_base.attr(name) = value;
+        m_base.attr(std::move(name)) = std::move(value);
     }
 
     PYBIND11_NOINLINE void export_values() {
@@ -2610,7 +2610,7 @@ PYBIND11_NOINLINE void print(const tuple &args, const dict &kwargs) {
     }
 
     auto write = file.attr("write");
-    write(line);
+    write(std::move(line));
     write(kwargs.contains("end") ? kwargs["end"] : str("\n"));
 
     if (kwargs.contains("flush") && kwargs["flush"].cast<bool>()) {
diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 0c5690064..27807953b 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -85,7 +85,9 @@ public:
         or `object` subclass causes a call to ``__setitem__``.
     \endrst */
     item_accessor operator[](handle key) const;
-    /// See above (the only difference is that they key is provided as a string literal)
+    /// See above (the only difference is that the key's reference is stolen)
+    item_accessor operator[](object &&key) const;
+    /// See above (the only difference is that the key is provided as a string literal)
     item_accessor operator[](const char *key) const;
 
     /** \rst
@@ -95,7 +97,9 @@ public:
         or `object` subclass causes a call to ``setattr``.
     \endrst */
     obj_attr_accessor attr(handle key) const;
-    /// See above (the only difference is that they key is provided as a string literal)
+    /// See above (the only difference is that the key's reference is stolen)
+    obj_attr_accessor attr(object &&key) const;
+    /// See above (the only difference is that the key is provided as a string literal)
     str_attr_accessor attr(const char *key) const;
 
     /** \rst
@@ -684,7 +688,7 @@ public:
     }
     template <typename T>
     void operator=(T &&value) & {
-        get_cache() = reinterpret_borrow<object>(object_or_cast(std::forward<T>(value)));
+        get_cache() = ensure_object(object_or_cast(std::forward<T>(value)));
     }
 
     template <typename T = Policy>
@@ -712,6 +716,9 @@ public:
     }
 
 private:
+    static object ensure_object(object &&o) { return std::move(o); }
+    static object ensure_object(handle h) { return reinterpret_borrow<object>(h); }
+
     object &get_cache() const {
         if (!cache) {
             cache = Policy::get(obj, key);
@@ -1711,7 +1718,10 @@ public:
     size_t size() const { return (size_t) PyTuple_Size(m_ptr); }
     bool empty() const { return size() == 0; }
     detail::tuple_accessor operator[](size_t index) const { return {*this, index}; }
-    detail::item_accessor operator[](handle h) const { return object::operator[](h); }
+    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>
+    detail::item_accessor operator[](T &&o) const {
+        return object::operator[](std::forward<T>(o));
+    }
     detail::tuple_iterator begin() const { return {*this, 0}; }
     detail::tuple_iterator end() const { return {*this, PyTuple_GET_SIZE(m_ptr)}; }
 };
@@ -1771,7 +1781,10 @@ public:
     }
     bool empty() const { return size() == 0; }
     detail::sequence_accessor operator[](size_t index) const { return {*this, index}; }
-    detail::item_accessor operator[](handle h) const { return object::operator[](h); }
+    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>
+    detail::item_accessor operator[](T &&o) const {
+        return object::operator[](std::forward<T>(o));
+    }
     detail::sequence_iterator begin() const { return {*this, 0}; }
     detail::sequence_iterator end() const { return {*this, PySequence_Size(m_ptr)}; }
 };
@@ -1790,7 +1803,10 @@ public:
     size_t size() const { return (size_t) PyList_Size(m_ptr); }
     bool empty() const { return size() == 0; }
     detail::list_accessor operator[](size_t index) const { return {*this, index}; }
-    detail::item_accessor operator[](handle h) const { return object::operator[](h); }
+    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>
+    detail::item_accessor operator[](T &&o) const {
+        return object::operator[](std::forward<T>(o));
+    }
     detail::list_iterator begin() const { return {*this, 0}; }
     detail::list_iterator end() const { return {*this, PyList_GET_SIZE(m_ptr)}; }
     template <typename T>
@@ -2090,6 +2106,10 @@ item_accessor object_api<D>::operator[](handle key) const {
     return {derived(), reinterpret_borrow<object>(key)};
 }
 template <typename D>
+item_accessor object_api<D>::operator[](object &&key) const {
+    return {derived(), std::move(key)};
+}
+template <typename D>
 item_accessor object_api<D>::operator[](const char *key) const {
     return {derived(), pybind11::str(key)};
 }
@@ -2098,6 +2118,10 @@ obj_attr_accessor object_api<D>::attr(handle key) const {
     return {derived(), reinterpret_borrow<object>(key)};
 }
 template <typename D>
+obj_attr_accessor object_api<D>::attr(object &&key) const {
+    return {derived(), std::move(key)};
+}
+template <typename D>
 str_attr_accessor object_api<D>::attr(const char *key) const {
     return {derived(), key};
 }
diff --git a/include/pybind11/stl.h b/include/pybind11/stl.h
index 597bce61d..ab30ecac0 100644
--- a/include/pybind11/stl.h
+++ b/include/pybind11/stl.h
@@ -128,7 +128,7 @@ struct map_caster {
             if (!key || !value) {
                 return handle();
             }
-            d[key] = value;
+            d[std::move(key)] = std::move(value);
         }
         return d.release();
     }
diff --git a/tests/test_pytypes.cpp b/tests/test_pytypes.cpp
index ef214acc3..cb81007c3 100644
--- a/tests/test_pytypes.cpp
+++ b/tests/test_pytypes.cpp
@@ -661,4 +661,38 @@ TEST_SUBMODULE(pytypes, m) {
         double v = x.get_value();
         return v * v;
     });
+
+    m.def("tuple_rvalue_getter", [](const py::tuple &tup) {
+        // tests accessing tuple object with rvalue int
+        for (size_t i = 0; i < tup.size(); i++) {
+            auto o = py::handle(tup[py::int_(i)]);
+            if (!o) {
+                throw py::value_error("tuple is malformed");
+            }
+        }
+        return tup;
+    });
+    m.def("list_rvalue_getter", [](const py::list &l) {
+        // tests accessing list with rvalue int
+        for (size_t i = 0; i < l.size(); i++) {
+            auto o = py::handle(l[py::int_(i)]);
+            if (!o) {
+                throw py::value_error("list is malformed");
+            }
+        }
+        return l;
+    });
+    m.def("populate_dict_rvalue", [](int population) {
+        auto d = py::dict();
+        for (int i = 0; i < population; i++) {
+            d[py::int_(i)] = py::int_(i);
+        }
+        return d;
+    });
+    m.def("populate_obj_str_attrs", [](py::object &o, int population) {
+        for (int i = 0; i < population; i++) {
+            o.attr(py::str(py::int_(i))) = py::str(py::int_(i));
+        }
+        return o;
+    });
 }
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index b91a7e156..3e9d51a27 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -1,5 +1,6 @@
 import contextlib
 import sys
+import types
 
 import pytest
 
@@ -320,8 +321,7 @@ def test_accessors():
 def test_accessor_moves():
     inc_refs = m.accessor_moves()
     if inc_refs:
-        # To be changed in PR #3970: [1, 0, 1, 0, ...]
-        assert inc_refs == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+        assert inc_refs == [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
     else:
         pytest.skip("Not defined: PYBIND11_HANDLE_REF_DEBUG")
 
@@ -707,3 +707,30 @@ def test_implementation_details():
 def test_external_float_():
     r1 = m.square_float_(2.0)
     assert r1 == 4.0
+
+
+def test_tuple_rvalue_getter():
+    pop = 1000
+    tup = tuple(range(pop))
+    m.tuple_rvalue_getter(tup)
+
+
+def test_list_rvalue_getter():
+    pop = 1000
+    my_list = list(range(pop))
+    m.list_rvalue_getter(my_list)
+
+
+def test_populate_dict_rvalue():
+    pop = 1000
+    my_dict = {i: i for i in range(pop)}
+    assert m.populate_dict_rvalue(pop) == my_dict
+
+
+def test_populate_obj_str_attrs():
+    pop = 1000
+    o = types.SimpleNamespace(**{str(i): i for i in range(pop)})
+    new_o = m.populate_obj_str_attrs(o, pop)
+    new_attrs = {k: v for k, v in new_o.__dict__.items() if not k.startswith("_")}
+    assert all(isinstance(v, str) for v in new_attrs.values())
+    assert len(new_attrs) == pop