diff --git a/src/xdoctest/__main__.pyi b/src/xdoctest/__main__.pyi
index af9cafae..419f63f6 100644
--- a/src/xdoctest/__main__.pyi
+++ b/src/xdoctest/__main__.pyi
@@ -1,6 +1,8 @@
 from typing import Union
 from typing import List
 
+__tests__: str
+
 
 def main(argv: Union[List[str], None] = None):
     ...
diff --git a/src/xdoctest/constants.pyi b/src/xdoctest/constants.pyi
index 561290a0..a7ba3d95 100644
--- a/src/xdoctest/constants.pyi
+++ b/src/xdoctest/constants.pyi
@@ -24,4 +24,4 @@ class _NOT_EVAL_TYPE:
     __nonzero__: Incomplete
 
 
-NOT_EVALED: Incomplete
+NOT_EVALED: _NOT_EVAL_TYPE
diff --git a/src/xdoctest/runner.pyi b/src/xdoctest/runner.pyi
index 44ea3ac3..617d50fd 100644
--- a/src/xdoctest/runner.pyi
+++ b/src/xdoctest/runner.pyi
@@ -4,9 +4,11 @@ from types import ModuleType
 from typing import List
 from typing import Dict
 from typing import Any
+from typing import Set
+from _typeshed import Incomplete
 
 
-def log(msg: str, verbose: int) -> None:
+def log(msg: str, verbose: int, level: int = 1) -> None:
     ...
 
 
@@ -14,13 +16,24 @@ def doctest_callable(func: Callable) -> None:
     ...
 
 
+def gather_doctests(doctest_identifiers,
+                    style: str = ...,
+                    analysis: str = ...,
+                    verbose: Incomplete | None = ...) -> None:
+    ...
+
+
 def doctest_module(module_identifier: Union[str, ModuleType, None] = None,
                    command: str = None,
                    argv: Union[List[str], None] = None,
                    exclude: List[str] = ...,
-                   style: str = ...,
+                   style: str = 'auto',
                    verbose: Union[int, None] = None,
                    config: Dict[str, object] = None,
                    durations: Union[int, None] = None,
                    analysis: str = 'auto') -> Dict[str, Any]:
     ...
+
+
+def undefined_names(sourcecode: str) -> Set[str]:
+    ...
diff --git a/src/xdoctest/static_analysis.pyi b/src/xdoctest/static_analysis.pyi
index c4903ddc..ef72bf7f 100644
--- a/src/xdoctest/static_analysis.pyi
+++ b/src/xdoctest/static_analysis.pyi
@@ -81,7 +81,9 @@ def parse_calldefs(source: Incomplete | None = ...,
     ...
 
 
-def parse_static_value(key: str, source: str = None, fpath: str = None):
+def parse_static_value(key: str,
+                       source: str = None,
+                       fpath: str = None) -> object:
     ...
 
 
@@ -101,7 +103,8 @@ def is_balanced_statement(lines: List[str],
     ...
 
 
-def extract_comments(source: str) -> Generator[Any, None, Any]:
+def extract_comments(
+        source: Union[str, List[str]]) -> Generator[Any, None, Any]:
     ...
 
 
diff --git a/src/xdoctest/utils/util_import.pyi b/src/xdoctest/utils/util_import.pyi
index 2080b71d..497720ce 100644
--- a/src/xdoctest/utils/util_import.pyi
+++ b/src/xdoctest/utils/util_import.pyi
@@ -1,5 +1,8 @@
+from typing import Union
 from os import PathLike
 from types import ModuleType
+from typing import List
+from typing import Tuple
 from _typeshed import Incomplete
 
 
@@ -23,7 +26,8 @@ class PythonPathContext:
         ...
 
 
-def import_module_from_path(modpath: PathLike, index: int = ...) -> ModuleType:
+def import_module_from_path(modpath: Union[str, PathLike],
+                            index: int = ...) -> ModuleType:
     ...
 
 
@@ -31,16 +35,18 @@ def import_module_from_name(modname: str) -> ModuleType:
     ...
 
 
-def modname_to_modpath(modname: str,
-                       hide_init: bool = True,
-                       hide_main: bool = False,
-                       sys_path: list = None) -> str:
+def modname_to_modpath(
+        modname: str,
+        hide_init: bool = True,
+        hide_main: bool = False,
+        sys_path: Union[None, List[Union[str,
+                                         PathLike]]] = None) -> str | None:
     ...
 
 
-def normalize_modpath(modpath: PathLike,
+def normalize_modpath(modpath: Union[str, PathLike],
                       hide_init: bool = True,
-                      hide_main: bool = False) -> PathLike:
+                      hide_main: bool = False) -> str | PathLike:
     ...
 
 
@@ -52,5 +58,5 @@ def modpath_to_modname(modpath: str,
     ...
 
 
-def split_modpath(modpath: str, check: bool = True) -> tuple:
+def split_modpath(modpath: str, check: bool = True) -> Tuple[str, str]:
     ...