diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 0b4f46f6d..35f5c13ba 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -493,7 +493,11 @@ protected:
                 } else {
                     std::string tname(t->name());
                     detail::clean_type_id(tname);
-                    signature += "Annotated[Any, \"" + tname + "\"]";
+                    if (detail::cpp_name_needs_typing_annotated(tname.c_str())) {
+                        signature += "Annotated[Any, \"" + tname + "\"]";
+                    } else {
+                        signature += tname;
+                    }
                 }
             } else {
                 signature += c;
diff --git a/include/pybind11/typing.h b/include/pybind11/typing.h
index b7b1a4e54..6c2bea28a 100644
--- a/include/pybind11/typing.h
+++ b/include/pybind11/typing.h
@@ -113,5 +113,15 @@ struct handle_type_name<typing::Callable<Return(Args...)>> {
                                  + const_name("]");
 };
 
+inline bool cpp_name_needs_typing_annotated(const char *cpp_name) {
+    while (*cpp_name) {
+        char c = *cpp_name++;
+        if (c == ':' || c == '<') { // Assuming valid names, there is no need to check for '>'.
+            return true;
+        }
+    }
+    return false;
+}
+
 PYBIND11_NAMESPACE_END(detail)
 PYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)