diff --git a/src/cockpit/transports.py b/src/cockpit/transports.py
index faa7aaee3494..8aabc7d83d6b 100644
--- a/src/cockpit/transports.py
+++ b/src/cockpit/transports.py
@@ -29,14 +29,14 @@
 import struct
 import subprocess
 import termios
-from typing import Any, ClassVar, Deque, Dict, List, Optional, Sequence, Tuple
+from typing import Any, ClassVar, Sequence
 
 from .jsonutil import JsonObject, get_int
 
 libc6 = ctypes.cdll.LoadLibrary('libc.so.6')
 
 
-def prctl(*args):
+def prctl(*args: int) -> None:
     if libc6.prctl(*args) != 0:
         raise OSError('prctl() failed')
 
@@ -55,7 +55,7 @@ class _Transport(asyncio.Transport):
     _loop: asyncio.AbstractEventLoop
     _protocol: asyncio.Protocol
 
-    _queue: Optional[Deque[bytes]]
+    _queue: 'collections.deque[bytes] | None'
     _in_fd: int
     _out_fd: int
     _closing: bool
@@ -67,7 +67,7 @@ def __init__(self,
                  loop: asyncio.AbstractEventLoop,
                  protocol: asyncio.Protocol,
                  in_fd: int = -1, out_fd: int = -1,
-                 extra: Optional[Dict[str, object]] = None):
+                 extra: 'dict[str, object] | None' = None):
         super().__init__(extra)
 
         self._loop = loop
@@ -138,7 +138,7 @@ def resume_reading(self) -> None:
     def _close(self) -> None:
         pass
 
-    def abort(self, exc: Optional[Exception] = None) -> None:
+    def abort(self, exc: 'Exception | None' = None) -> None:
         self._closing = True
         self._close_reader()
         self._remove_write_queue()
@@ -162,10 +162,10 @@ def get_write_buffer_size(self) -> int:
             return 0
         return sum(len(block) for block in self._queue)
 
-    def get_write_buffer_limits(self) -> Tuple[int, int]:
+    def get_write_buffer_limits(self) -> 'tuple[int, int]':
         return (0, 0)
 
-    def set_write_buffer_limits(self, high: Optional[int] = None, low: Optional[int] = None) -> None:
+    def set_write_buffer_limits(self, high: 'int | None' = None, low: 'int | None' = None) -> None:
         assert high is None or high == 0
         assert low is None or low == 0
 
@@ -305,11 +305,11 @@ class SubprocessTransport(_Transport, asyncio.SubprocessTransport):
     data from it, making it available via the .get_stderr() method.
     """
 
-    _returncode: Optional[int] = None
+    _returncode: 'int | None' = None
 
-    _pty_fd: Optional[int] = None
-    _process: Optional['subprocess.Popen[bytes]'] = None
-    _stderr: Optional['Spooler']
+    _pty_fd: 'int | None' = None
+    _process: 'subprocess.Popen[bytes] | None' = None
+    _stderr: 'Spooler | None'
 
     @staticmethod
     def _create_watcher() -> asyncio.AbstractChildWatcher:
@@ -363,11 +363,11 @@ def __init__(self,
                  args: Sequence[str],
                  *,
                  pty: bool = False,
-                 window: Optional[WindowSize] = None,
+                 window: 'WindowSize | None' = None,
                  **kwargs: Any):
 
         # go down as a team -- we don't want any leaked processes when the bridge terminates
-        def preexec_fn():
+        def preexec_fn() -> None:
             prctl(SET_PDEATHSIG, signal.SIGTERM)
             if pty:
                 fcntl.ioctl(0, termios.TIOCSCTTY, 0)
@@ -422,7 +422,7 @@ def get_pid(self) -> int:
         assert self._process is not None
         return self._process.pid
 
-    def get_returncode(self) -> Optional[int]:
+    def get_returncode(self) -> 'int | None':
         return self._returncode
 
     def get_pipe_transport(self, fd: int) -> asyncio.Transport:
@@ -502,7 +502,7 @@ class Spooler:
 
     _loop: asyncio.AbstractEventLoop
     _fd: int
-    _contents: List[bytes]
+    _contents: 'list[bytes]'
 
     def __init__(self, loop: asyncio.AbstractEventLoop, fd: int):
         self._loop = loop
diff --git a/test/static-code b/test/static-code
index f5e7eee985a6..f1eb2bf323be 100755
--- a/test/static-code
+++ b/test/static-code
@@ -49,6 +49,7 @@ if [ "${WITH_PARTIAL_TREE:-0}" = 0 ]; then
         src/cockpit/_version.py
         src/cockpit/jsonutil.py
         src/cockpit/protocol.py
+        src/cockpit/transports.py
     '
     test_mypy() {
         command -v mypy >/dev/null || skip 'no mypy'