diff --git a/pybind11_stubgen/parser/mixins/fix.py b/pybind11_stubgen/parser/mixins/fix.py
index 2a3a17b..4d7756f 100644
--- a/pybind11_stubgen/parser/mixins/fix.py
+++ b/pybind11_stubgen/parser/mixins/fix.py
@@ -144,6 +144,11 @@ def handle_value(self, value: Any) -> Value:
         result = super().handle_value(value)
         if inspect.isroutine(value) and result.is_print_safe:
             self._add_import(QualifiedName.from_str(result.repr))
+        else:
+            type_ = type(value)
+            self._add_import(
+                QualifiedName.from_str(f"{type_.__module__}.{type_.__qualname__}")
+            )
         return result
 
     def parse_annotation_str(
@@ -159,7 +164,9 @@ def _add_import(self, name: QualifiedName) -> None:
             return
         if len(name) == 1 and len(name[0]) == 0:
             return
-        if hasattr(builtins, name[0]):
+        if len(name) == 1 and hasattr(builtins, name[0]):
+            return
+        if len(name) > 0 and name[0] == "builtins":
             return
         if self.__current_class is not None and hasattr(self.__current_class, name[0]):
             return
@@ -171,6 +178,8 @@ def _add_import(self, name: QualifiedName) -> None:
         if module_name is None:
             self.report_error(NameResolutionError(name))
             return
+        if self.__current_module.__name__ == str(module_name):
+            return
         self.__extra_imports.add(Import(name=None, origin=module_name))
 
     def _get_parent_module(self, name: QualifiedName) -> QualifiedName | None:
@@ -913,8 +922,6 @@ def parse_annotation_str(
             except ValueError:
                 pass
             else:
-                # call `handle_type` to trigger implicit import
-                self.handle_type(FixedSize)
                 return self.handle_value(FixedSize(*dimensions))
         return result