diff --git a/changelog.d/14671.misc b/changelog.d/14671.misc
new file mode 100644
index 000000000000..93ceaeafc9b9
--- /dev/null
+++ b/changelog.d/14671.misc
@@ -0,0 +1 @@
+Improve type hints.
diff --git a/mypy.ini b/mypy.ini
index a4a1e4511a07..727536df50fd 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -12,6 +12,7 @@ local_partial_types = True
 no_implicit_optional = True
 disallow_untyped_defs = True
 strict_equality = True
+warn_redundant_casts = True
 
 files =
   docker/,
diff --git a/scripts-dev/release.py b/scripts-dev/release.py
index bf47b6c713ff..6974fd789575 100755
--- a/scripts-dev/release.py
+++ b/scripts-dev/release.py
@@ -27,7 +27,7 @@
 import urllib.request
 from os import path
 from tempfile import TemporaryDirectory
-from typing import Any, List, Optional, cast
+from typing import Any, List, Optional
 
 import attr
 import click
@@ -174,9 +174,7 @@ def _prepare() -> None:
         click.get_current_context().abort()
 
     # Switch to the release branch.
-    # Cast safety: parse() won't return a version.LegacyVersion from our
-    # version string format.
-    parsed_new_version = cast(version.Version, version.parse(new_version))
+    parsed_new_version = version.parse(new_version)
 
     # We assume for debian changelogs that we only do RCs or full releases.
     assert not parsed_new_version.is_devrelease
diff --git a/synapse/storage/database.py b/synapse/storage/database.py
index 55bcb90001e9..0b29e67b9447 100644
--- a/synapse/storage/database.py
+++ b/synapse/storage/database.py
@@ -667,7 +667,8 @@ def new_transaction(
                 )
         # also check variables referenced in func's closure
         if inspect.isfunction(func):
-            f = cast(types.FunctionType, func)
+            # Keep the cast for now---it helps PyCharm to understand what `func` is.
+            f = cast(types.FunctionType, func)  # type: ignore[redundant-cast]
             if f.__closure__:
                 for i, cell in enumerate(f.__closure__):
                     if inspect.isgenerator(cell.cell_contents):
diff --git a/synapse/storage/engines/postgres.py b/synapse/storage/engines/postgres.py
index 719a51733621..f9f562ea4544 100644
--- a/synapse/storage/engines/postgres.py
+++ b/synapse/storage/engines/postgres.py
@@ -77,7 +77,7 @@ def check_database(
         # docs: The number is formed by converting the major, minor, and
         # revision numbers into two-decimal-digit numbers and appending them
         # together. For example, version 8.1.5 will be returned as 80105
-        self._version = cast(int, db_conn.server_version)
+        self._version = db_conn.server_version
         allow_unsafe_locale = self.config.get("allow_unsafe_locale", False)
 
         # Are we on a supported PostgreSQL version?