diff --git a/jedi/api/environment.py b/jedi/api/environment.py
index aea96c47..b2fc5b2c 100644
--- a/jedi/api/environment.py
+++ b/jedi/api/environment.py
@@ -15,7 +15,7 @@ from jedi.inference.compiled.subprocess import CompiledSubprocess, \
 
 import parso
 
-_VersionInfo = namedtuple('VersionInfo', 'major minor micro')
+_VersionInfo = namedtuple('VersionInfo', 'major minor micro')  # type: ignore[name-match]
 
 _SUPPORTED_PYTHONS = ['3.10', '3.9', '3.8', '3.7', '3.6']
 _SAFE_PATHS = ['/usr/bin', '/usr/local/bin']
@@ -384,8 +384,7 @@ def _get_executable_path(path, safe=True):
 
 
 def _get_executables_from_windows_registry(version):
-    # https://github.com/python/typeshed/pull/3794 adds winreg
-    import winreg  # type: ignore[import]
+    import winreg
 
     # TODO: support Python Anaconda.
     sub_keys = [
diff --git a/jedi/api/keywords.py b/jedi/api/keywords.py
index 95c49227..80ff13c3 100644
--- a/jedi/api/keywords.py
+++ b/jedi/api/keywords.py
@@ -5,8 +5,7 @@ from typing import Dict, Optional
 from jedi.inference.names import AbstractArbitraryName
 
 try:
-    # https://github.com/python/typeshed/pull/4351 adds pydoc_data
-    from pydoc_data import topics  # type: ignore[import]
+    from pydoc_data import topics
     pydoc_topics: Optional[Dict[str, str]] = topics.topics
 except ImportError:
     # Python 3.6.8 embeddable does not have pydoc_data.
diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index 91f2da08..f09dd5e7 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -40,7 +40,7 @@ NOT_CLASS_TYPES = (
 MethodDescriptorType = type(str.replace)
 WrapperDescriptorType = type(set.__iter__)
 # `object.__subclasshook__` is an already executed descriptor.
-object_class_dict = type.__dict__["__dict__"].__get__(object)
+object_class_dict = type.__dict__["__dict__"].__get__(object)  # type: ignore[index]
 ClassMethodDescriptorType = type(object_class_dict['__subclasshook__'])
 
 _sentinel = object()
diff --git a/jedi/utils.py b/jedi/utils.py
index b7e1c1a8..dd529be7 100644
--- a/jedi/utils.py
+++ b/jedi/utils.py
@@ -2,7 +2,7 @@
 Utilities for end-users.
 """
 
-import __main__  # type: ignore[import]
+import __main__
 from collections import namedtuple
 import logging
 import traceback
diff --git a/setup.cfg b/setup.cfg
index 98a775aa..4347bbf7 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -28,6 +28,9 @@ max-line-length = 100
 
 
 [mypy]
+# Exclude our copies of external stubs
+exclude = ^jedi/third_party
+
 # Ensure generics are explicit about what they are (e.g: `List[str]` rather than
 # just `List`)
 disallow_any_generics = True
diff --git a/setup.py b/setup.py
index 5b04c3ce..23b147e5 100755
--- a/setup.py
+++ b/setup.py
@@ -45,7 +45,10 @@ setup(name='jedi',
           ],
           'qa': [
               'flake8==3.8.3',
-              'mypy==0.782',
+              # latest version supporting Python 3.6
+              'mypy==0.971',
+              # Arbitrary pins, latest at the time of pinning
+              'types-setuptools==67.2.0.1',
           ],
           'docs': [
               # Just pin all of these.