diff --git a/lxml-stubs/etree.pyi b/lxml-stubs/etree.pyi
index bae7f34..50d412a 100644
--- a/lxml-stubs/etree.pyi
+++ b/lxml-stubs/etree.pyi
@@ -524,21 +524,21 @@ def cleanup_namespaces(
 def parse(
     source: _FileSource,
     parser: Optional[_AnyParser] = ...,
-    base_url: _AnyStr = ...,
+    base_url: Optional[_AnyStr] = ...,
 ) -> Union[_ElementTree, Any]: ...
 @overload
 def fromstring(
     text: _AnyStr,
     parser: None = ...,
     *,
-    base_url: _AnyStr = ...,
+    base_url: Optional[_AnyStr] = ...,
 ) -> _Element: ...
 @overload
 def fromstring(
     text: _AnyStr,
     parser: _AnyParser = ...,
     *,
-    base_url: _AnyStr = ...,
+    base_url: Optional[_AnyStr] = ...,
 ) -> Union[_Element, Any]: ...
 @overload
 def tostring(
diff --git a/lxml-stubs/html/__init__.pyi b/lxml-stubs/html/__init__.pyi
index 65da1ea..5ebbcff 100644
--- a/lxml-stubs/html/__init__.pyi
+++ b/lxml-stubs/html/__init__.pyi
@@ -49,7 +49,7 @@ class HtmlMixin:
     def cssselect(self, expr: str, translator: str = ...) -> List["_Element"]: ...
     def make_links_absolute(
         self,
-        base_url: str = ...,
+        base_url: Optional[str] = ...,
         resolve_base_href: bool = ...,
         handle_failures: _HANDLE_FALURES = ...,
     ) -> str: ...
@@ -59,7 +59,7 @@ class HtmlMixin:
         self,
         link_repl_func: Callable[[str], Optional[str]],
         resolve_base_href: bool = ...,
-        base_href: str = ...,
+        base_href: Optional[str] = ...,
     ) -> None: ...
     def __getattr__(self, name: str) -> Any: ...  # incomplete
 
@@ -75,11 +75,11 @@ def document_fromstring(
 def fragments_fromstring(
     html: "_AnyStr",
     no_leading_text: bool = ...,
-    base_url: str = ...,
+    base_url: Optional[str] = ...,
     parser: "_BaseParser" = ...,
     **kw
 ) -> "_Element": ...
 def fromstring(
-    html: "_AnyStr", base_url: str = ..., parser: "_BaseParser" = ..., **kw
+    html: "_AnyStr", base_url: Optional[str] = ..., parser: "_BaseParser" = ..., **kw
 ) -> "_Element": ...
 def __getattr__(name: str) -> Any: ...  # incomplete
diff --git a/lxml-stubs/objectify.pyi b/lxml-stubs/objectify.pyi
index 18303d8..30e007a 100644
--- a/lxml-stubs/objectify.pyi
+++ b/lxml-stubs/objectify.pyi
@@ -1,4 +1,4 @@
-from typing import Any, Union
+from typing import Any, Optional, Union
 
 from lxml.etree import ElementBase, XMLParser
 
@@ -12,5 +12,5 @@ def fromstring(
     text: Union[bytes, str],
     parser: XMLParser = ...,
     *,
-    base_url: Union[bytes, str] = ...
+    base_url: Optional[Union[bytes, str]] = ...
 ) -> ObjectifiedElement: ...