diff --git a/aiosqlite/core.py b/aiosqlite/core.py
index 58c227d..58c3fec 100644
--- a/aiosqlite/core.py
+++ b/aiosqlite/core.py
@@ -10,9 +10,8 @@
 import sqlite3
 from functools import partial
 from pathlib import Path
-from queue import Empty, Queue
+from queue import Empty, Queue, SimpleQueue
 from threading import Thread
-
 from typing import (
     Any,
     AsyncIterator,
@@ -21,6 +20,7 @@
     Iterable,
     Literal,
     Optional,
+    Tuple,
     Type,
     Union,
 )
@@ -37,6 +37,21 @@
 IsolationLevel = Optional[Literal["DEFERRED", "IMMEDIATE", "EXCLUSIVE"]]
 
 
+def set_result(fut: asyncio.Future, result: Any) -> None:
+    """Set the result of a future if it hasn't been set already."""
+    if not fut.done():
+        fut.set_result(result)
+
+
+def set_exception(fut: asyncio.Future, e: BaseException) -> None:
+    """Set the exception of a future if it hasn't been set already."""
+    if not fut.done():
+        fut.set_exception(e)
+
+
+_STOP_RUNNING_SENTINEL = object()
+
+
 class Connection(Thread):
     def __init__(
         self,
@@ -48,7 +63,7 @@ def __init__(
         self._running = True
         self._connection: Optional[sqlite3.Connection] = None
         self._connector = connector
-        self._tx: Queue = Queue()
+        self._tx: SimpleQueue[Tuple[asyncio.Future, Callable[[], Any]]] = SimpleQueue()
         self._iter_chunk_size = iter_chunk_size
 
         if loop is not None:
@@ -57,6 +72,11 @@ def __init__(
                 DeprecationWarning,
             )
 
+    def _stop_running(self):
+        self._running = False
+        # PEP 661 is not accepted yet, so we cannot type a sentinel
+        self._tx.put_nowait(_STOP_RUNNING_SENTINEL)  # type: ignore[arg-type]
+
     @property
     def _conn(self) -> sqlite3.Connection:
         if self._connection is None:
@@ -83,29 +103,20 @@ def run(self) -> None:
             # Continues running until all queue items are processed,
             # even after connection is closed (so we can finalize all
             # futures)
-            try:
-                future, function = self._tx.get(timeout=0.1)
-            except Empty:
-                if self._running:
-                    continue
+
+            tx_item = self._tx.get()
+            if tx_item is _STOP_RUNNING_SENTINEL:
                 break
+
+            future, function = tx_item
+
             try:
                 LOG.debug("executing %s", function)
                 result = function()
                 LOG.debug("operation %s completed", function)
-
-                def set_result(fut, result):
-                    if not fut.done():
-                        fut.set_result(result)
-
                 future.get_loop().call_soon_threadsafe(set_result, future, result)
             except BaseException as e:  # noqa B036
                 LOG.debug("returning exception %s", e)
-
-                def set_exception(fut, e):
-                    if not fut.done():
-                        fut.set_exception(e)
-
                 future.get_loop().call_soon_threadsafe(set_exception, future, e)
 
     async def _execute(self, fn, *args, **kwargs):
@@ -128,7 +139,7 @@ async def _connect(self) -> "Connection":
                 self._tx.put_nowait((future, self._connector))
                 self._connection = await future
             except Exception:
-                self._running = False
+                self._stop_running()
                 self._connection = None
                 raise
 
@@ -169,7 +180,7 @@ async def close(self) -> None:
             LOG.info("exception occurred while closing connection")
             raise
         finally:
-            self._running = False
+            self._stop_running()
             self._connection = None
 
     @contextmanager