diff --git a/tools/provision b/tools/provision
index 6f1d7546..6ec9015b 100755
--- a/tools/provision
+++ b/tools/provision
@@ -16,7 +16,7 @@ end_format = "\033[0m"
 bold = "\033[1m"
 
 
-def main():
+def main() -> None:
     usage = """./tools/provision
 
 Creates a Python virtualenv. Its Python version is equal to
@@ -94,7 +94,7 @@ the Python version this command is executed with."""
     # In order to install all required packages for the venv, `pip` needs to be executed by
     # the venv's Python interpreter. `--prefix venv_dir` ensures that all modules are installed
     # in the right place.
-    def install_dependencies(requirements_filename):
+    def install_dependencies(requirements_filename: str) -> None:
         pip_path = os.path.join(venv_dir, venv_exec_dir, "pip")
         # We first install a modern version of pip that supports --prefix
         subprocess.call([pip_path, "install", "pip>=10"])
diff --git a/tools/run-mypy b/tools/run-mypy
index ddd911e1..cd8501ce 100755
--- a/tools/run-mypy
+++ b/tools/run-mypy
@@ -4,9 +4,8 @@ import argparse
 import os
 import subprocess
 import sys
-from collections import OrderedDict
 from pathlib import PurePath
-from typing import Dict, List, cast
+from typing import List, OrderedDict
 
 from zulint import lister
 
@@ -25,7 +24,6 @@ exclude = [
     # Excluded out of laziness:
     "zulip_bots/zulip_bots/simple_lib.py",
     "zulip_bots/zulip_bots/tests/test_lib.py",
-    "tools",
 ]
 
 # These files will be included even if excluded by a rule above.
@@ -93,8 +91,6 @@ force_include = [
     "zulip_bots/zulip_bots/bots/susi/test_susi.py",
     "zulip_bots/zulip_bots/bots/front/front.py",
     "zulip_bots/zulip_bots/bots/front/test_front.py",
-    "tools/custom_check.py",
-    "tools/deploy",
 ]
 
 parser = argparse.ArgumentParser(description="Run mypy on files tracked by git.")
@@ -154,17 +150,14 @@ if args.all:
     exclude = []
 
 # find all non-excluded files in current directory
-files_dict = cast(
-    Dict[str, List[str]],
-    lister.list_files(
-        targets=args.targets,
-        ftypes=["py", "pyi"],
-        use_shebang=True,
-        modified_only=args.modified,
-        exclude=exclude + ["stubs"],
-        group_by_ftype=True,
-        extless_only=args.scripts_only,
-    ),
+files_dict = lister.list_files(
+    targets=args.targets,
+    ftypes=["py", "pyi"],
+    use_shebang=True,
+    modified_only=args.modified,
+    exclude=exclude + ["stubs"],
+    group_by_ftype=True,
+    extless_only=args.scripts_only,
 )
 
 for inpath in force_include:
@@ -179,7 +172,7 @@ python_files = [
     fpath for fpath in files_dict["py"] if not fpath.endswith(".py") or fpath + "i" not in pyi_files
 ]
 
-repo_python_files = OrderedDict(
+repo_python_files = OrderedDict[str, List[str]](
     [("zulip", []), ("zulip_bots", []), ("zulip_botserver", []), ("tools", [])]
 )
 for file_path in python_files: