diff --git a/stdlib/2and3/xml/dom/minidom.pyi b/stdlib/2and3/xml/dom/minidom.pyi
index cb53e949889c..7a6eb192b384 100644
--- a/stdlib/2and3/xml/dom/minidom.pyi
+++ b/stdlib/2and3/xml/dom/minidom.pyi
@@ -1,6 +1,6 @@
-from typing import Any, Optional
+from typing import Any, Optional, Text, Union
 from xml.sax.xmlreader import XMLReader
 
 def parse(file: str, parser: Optional[XMLReader] = ..., bufsize: Optional[int] = ...): ...
-def parseString(string: str, parser: Optional[XMLReader] = ...): ...
+def parseString(string: Union[bytes, Text], parser: Optional[XMLReader] = ...): ...
 def __getattr__(name: str) -> Any: ...  # incomplete
diff --git a/stdlib/3/concurrent/futures/_base.pyi b/stdlib/3/concurrent/futures/_base.pyi
index 140f0a9b3142..ca4087948c3e 100644
--- a/stdlib/3/concurrent/futures/_base.pyi
+++ b/stdlib/3/concurrent/futures/_base.pyi
@@ -85,13 +85,13 @@ class Executor:
 def as_completed(fs: Iterable[Future[_T]], timeout: Optional[float] = ...) -> Iterator[Future[_T]]: ...
 
 # Ideally this would be a namedtuple, but mypy doesn't support generic tuple types. See #1976
-class DoneAndNotDoneFutures(Sequence[_T]):
+class DoneAndNotDoneFutures(Sequence[Set[Future[_T]]]):
     done: Set[Future[_T]]
     not_done: Set[Future[_T]]
     def __new__(_cls, done: Set[Future[_T]], not_done: Set[Future[_T]]) -> DoneAndNotDoneFutures[_T]: ...
     def __len__(self) -> int: ...
     @overload
-    def __getitem__(self, i: int) -> _T: ...
+    def __getitem__(self, i: int) -> Set[Future[_T]]: ...
     @overload
     def __getitem__(self, s: slice) -> DoneAndNotDoneFutures[_T]: ...
 
diff --git a/third_party/2and3/markdown/postprocessors.pyi b/third_party/2and3/markdown/postprocessors.pyi
index 42cddc124a44..a75d1e89d3ac 100644
--- a/third_party/2and3/markdown/postprocessors.pyi
+++ b/third_party/2and3/markdown/postprocessors.pyi
@@ -5,7 +5,7 @@ from . import util
 def build_postprocessors(md, **kwargs): ...
 
 class Postprocessor(util.Processor):
-    def run(self, text) -> None: ...
+    def run(self, text) -> Any: ...
 
 class RawHtmlPostprocessor(Postprocessor):
     def isblocklevel(self, html): ...
diff --git a/third_party/2and3/markdown/treeprocessors.pyi b/third_party/2and3/markdown/treeprocessors.pyi
index a213600a6159..a1725a66633b 100644
--- a/third_party/2and3/markdown/treeprocessors.pyi
+++ b/third_party/2and3/markdown/treeprocessors.pyi
@@ -6,7 +6,7 @@ def build_treeprocessors(md, **kwargs): ...
 def isString(s): ...
 
 class Treeprocessor(util.Processor):
-    def run(self, root) -> None: ...
+    def run(self, root) -> Optional[Any]: ...
 
 class InlineProcessor(Treeprocessor):
     inlinePatterns: Any