diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index 4dcbf26236..7b014fed99 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -1401,7 +1401,7 @@ struct handle_type_name<buffer> {
 };
 template <>
 struct handle_type_name<int_> {
-    static constexpr auto name = io_name("typing.SupportsInt", "int");
+    static constexpr auto name = const_name("int");
 };
 template <>
 struct handle_type_name<iterable> {
@@ -1413,7 +1413,7 @@ struct handle_type_name<iterator> {
 };
 template <>
 struct handle_type_name<float_> {
-    static constexpr auto name = io_name("typing.SupportsFloat", "float");
+    static constexpr auto name = const_name("float");
 };
 template <>
 struct handle_type_name<function> {
@@ -1534,6 +1534,21 @@ struct pyobject_caster {
 template <typename T>
 class type_caster<T, enable_if_t<is_pyobject<T>::value>> : public pyobject_caster<T> {};
 
+template <>
+class type_caster<float_> : public pyobject_caster<float_> {
+public:
+    bool load(handle src, bool /* convert */) {
+        if (isinstance<float_>(src)) {
+            value = reinterpret_borrow<float_>(src);
+        } else if (isinstance<int_>(src)) {
+            value = float_(reinterpret_borrow<int_>(src));
+        } else {
+            return false;
+        }
+        return true;
+    }
+};
+
 // Our conditions for enabling moving are quite restrictive:
 // At compile time:
 // - T needs to be a non-const, non-pointer, non-reference type
diff --git a/tests/test_pytypes.cpp b/tests/test_pytypes.cpp
index 1c136cf0f2..7d5423e549 100644
--- a/tests/test_pytypes.cpp
+++ b/tests/test_pytypes.cpp
@@ -209,6 +209,7 @@ TEST_SUBMODULE(pytypes, m) {
     m.def("get_tuple_from_iterable", [](const py::iterable &iter) { return py::tuple(iter); });
     // test_float
     m.def("get_float", [] { return py::float_(0.0f); });
+    m.def("float_roundtrip", [](py::float_ f) { return f; });
     // test_list
     m.def("list_no_args", []() { return py::list{}; });
     m.def("list_ssize_t", []() { return py::list{(py::ssize_t) 0}; });
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index a199d72f0a..c1798f924c 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -61,6 +61,13 @@ def test_iterable(doc):
 
 def test_float(doc):
     assert doc(m.get_float) == "get_float() -> float"
+    assert doc(m.float_roundtrip) == "float_roundtrip(arg0: float) -> float"
+    f1 = m.float_roundtrip(5.5)
+    assert isinstance(f1, float)
+    assert f1 == 5.5
+    f2 = m.float_roundtrip(5)
+    assert isinstance(f2, float)
+    assert f2 == 5.0
 
 
 def test_list(capture, doc):
@@ -917,7 +924,7 @@ def test_inplace_rshift(a, b):
 def test_tuple_nonempty_annotations(doc):
     assert (
         doc(m.annotate_tuple_float_str)
-        == "annotate_tuple_float_str(arg0: tuple[typing.SupportsFloat, str]) -> None"
+        == "annotate_tuple_float_str(arg0: tuple[float, str]) -> None"
     )
 
 
@@ -930,7 +937,7 @@ def test_tuple_empty_annotations(doc):
 def test_tuple_variable_length_annotations(doc):
     assert (
         doc(m.annotate_tuple_variable_length)
-        == "annotate_tuple_variable_length(arg0: tuple[typing.SupportsFloat, ...]) -> None"
+        == "annotate_tuple_variable_length(arg0: tuple[float, ...]) -> None"
     )
 
 
@@ -989,7 +996,7 @@ def test_type_annotation(doc):
 def test_union_annotations(doc):
     assert (
         doc(m.annotate_union)
-        == "annotate_union(arg0: list[str | typing.SupportsInt | object], arg1: str, arg2: typing.SupportsInt, arg3: object) -> list[str | int | object]"
+        == "annotate_union(arg0: list[str | int | object], arg1: str, arg2: int, arg3: object) -> list[str | int | object]"
     )