diff --git a/src/bouncer/network.py b/src/bouncer/network.py
index f5d18b1..acbffcd 100644
--- a/src/bouncer/network.py
+++ b/src/bouncer/network.py
@@ -156,6 +156,7 @@ class Network:
         self._reconnect_attempt: int = 0
         self._running: bool = False
         self._read_task: asyncio.Task[None] | None = None
+        self._reconnect_task: asyncio.Task[None] | None = None
         self._probation_task: asyncio.Task[None] | None = None
         # Transient nick used during registration/probation
         self._connect_nick: str = ""
@@ -187,10 +188,9 @@ class Network:
     async def stop(self) -> None:
         """Disconnect and stop reconnection."""
         self._running = False
-        if self._read_task and not self._read_task.done():
-            self._read_task.cancel()
-        if self._probation_task and not self._probation_task.done():
-            self._probation_task.cancel()
+        for task in (self._read_task, self._reconnect_task, self._probation_task):
+            if task and not task.done():
+                task.cancel()
         await self._disconnect()
 
     async def send(self, msg: IRCMessage) -> None:
@@ -242,7 +242,7 @@ class Network:
             log.exception("[%s] connection failed", self.cfg.name)
             self.state = State.DISCONNECTED
             if self._running:
-                await self._schedule_reconnect()
+                self._schedule_reconnect()
 
     async def _disconnect(self) -> None:
         """Close the connection."""
@@ -259,7 +259,11 @@ class Network:
         self._reader = None
         self._writer = None
 
-    async def _schedule_reconnect(self) -> None:
+    def _schedule_reconnect(self) -> None:
+        """Schedule a reconnect after exponential backoff."""
+        self._reconnect_task = asyncio.create_task(self._reconnect_wait())
+
+    async def _reconnect_wait(self) -> None:
         """Wait with exponential backoff, then reconnect."""
         delay = BACKOFF_STEPS[min(self._reconnect_attempt, len(BACKOFF_STEPS) - 1)]
         self._reconnect_attempt += 1
@@ -267,7 +271,10 @@ class Network:
             "[%s] reconnecting in %ds (attempt %d)",
             self.cfg.name, delay, self._reconnect_attempt,
         )
-        await asyncio.sleep(delay)
+        try:
+            await asyncio.sleep(delay)
+        except asyncio.CancelledError:
+            return
         if self._running:
             await self._connect()
 
@@ -300,7 +307,7 @@ class Network:
         finally:
             await self._disconnect()
             if self._running:
-                await self._schedule_reconnect()
+                self._schedule_reconnect()
 
     async def _enter_probation(self) -> None:
         """Start probation period after registration. Survive = ready."""