diff --git a/include/pybind11/detail/type_caster_base.h b/include/pybind11/detail/type_caster_base.h
index 77f3d4790..1b3762167 100644
--- a/include/pybind11/detail/type_caster_base.h
+++ b/include/pybind11/detail/type_caster_base.h
@@ -1201,13 +1201,17 @@ protected:
     static Constructor make_move_constructor(...) { return nullptr; }
 };
 
+inline std::string annotated_any(const std::string &cpp_type) {
+    return "Annotated[Any, \"" + cpp_type + "\"]";
+}
+
 PYBIND11_NOINLINE std::string type_info_description(const std::type_info &ti) {
     if (auto *type_data = get_type_info(ti)) {
         handle th((PyObject *) type_data->type);
         return th.attr("__module__").cast<std::string>() + '.'
                + th.attr("__qualname__").cast<std::string>();
     }
-    return "Annotated[Any, \"" + clean_type_id(ti.name()) + "\"]";
+    return annotated_any(clean_type_id(ti.name()));
 }
 
 PYBIND11_NAMESPACE_END(detail)
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 33ad041fd..84b415a68 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -492,9 +492,7 @@ protected:
                     signature += rec->scope.attr("__module__").cast<std::string>() + "."
                                  + rec->scope.attr("__qualname__").cast<std::string>();
                 } else {
-                    std::string tname(t->name());
-                    detail::clean_type_id(tname);
-                    signature += "Annotated[Any, \"" + tname + "\"]";
+                    signature += detail::annotated_any(detail::clean_type_id(t->name()));
                 }
             } else {
                 signature += c;