diff --git a/aioesphomeapi/connection.py b/aioesphomeapi/connection.py
index f90a7e1..77506da 100644
--- a/aioesphomeapi/connection.py
+++ b/aioesphomeapi/connection.py
@@ -6,7 +6,18 @@ import socket
 import time
 from contextlib import suppress
 from dataclasses import astuple, dataclass
-from typing import Any, Callable, Coroutine, Dict, Iterable, List, Optional, Type, Union
+from typing import (
+    Any,
+    Callable,
+    Coroutine,
+    Dict,
+    Iterable,
+    List,
+    Optional,
+    Set,
+    Type,
+    Union,
+)
 
 import async_timeout
 from google.protobuf import message
@@ -127,7 +138,7 @@ class APIConnection:
         "_connect_complete",
         "_message_handlers",
         "log_name",
-        "_read_exception_handlers",
+        "_read_exception_futures",
         "_ping_timer",
         "_pong_timer",
         "_keep_alive_interval",
@@ -163,8 +174,8 @@ class APIConnection:
         # The friendly name to show for this connection in the logs
         self.log_name = log_name or params.address
 
-        # Handlers currently subscribed to exceptions in the read task
-        self._read_exception_handlers: List[Callable[[Exception], None]] = []
+        # futures currently subscribed to exceptions in the read task
+        self._read_exception_futures: Set[asyncio.Future[None]] = set()
 
         self._ping_timer: Optional[asyncio.TimerHandle] = None
         self._pong_timer: Optional[asyncio.TimerHandle] = None
@@ -601,7 +612,7 @@ class APIConnection:
 
         :raises TimeoutAPIError: if a timeout occured
         """
-        fut = self._loop.create_future()
+        fut: asyncio.Future[None] = self._loop.create_future()
         responses = []
 
         def on_message(resp: message.Message) -> None:
@@ -610,19 +621,12 @@ class APIConnection:
             if do_append(resp):
                 responses.append(resp)
             if do_stop(resp):
-                fut.set_result(responses)
-
-        def on_read_exception(exc: Exception) -> None:
-            if not fut.done():
-                new_exc = exc
-                if not isinstance(exc, APIConnectionError):
-                    new_exc = ReadFailedAPIError("Read failed")
-                    new_exc.__cause__ = exc
-                fut.set_exception(new_exc)
+                fut.set_result(None)
 
         for msg_type in msg_types:
             self._message_handlers.setdefault(msg_type, []).append(on_message)
-        self._read_exception_handlers.append(on_read_exception)
+
+        self._read_exception_futures.add(fut)
         # We must not await without a finally or
         # the message could fail to be removed if the
         # the await is cancelled
@@ -639,8 +643,7 @@ class APIConnection:
             for msg_type in msg_types:
                 with suppress(ValueError):
                     self._message_handlers[msg_type].remove(on_message)
-            with suppress(ValueError):
-                self._read_exception_handlers.remove(on_read_exception)
+            self._read_exception_futures.discard(fut)
 
         return responses
 
@@ -678,9 +681,15 @@ class APIConnection:
             )
         self._fatal_exception = err
         self._connection_state = ConnectionState.CLOSED
-        for handler in self._read_exception_handlers[:]:
-            handler(err)
-        self._read_exception_handlers.clear()
+        for fut in self._read_exception_futures:
+            if fut.done():
+                continue
+            new_exc = err
+            if not isinstance(err, APIConnectionError):
+                new_exc = ReadFailedAPIError("Read failed")
+                new_exc.__cause__ = err
+            fut.set_exception(new_exc)
+        self._read_exception_futures.clear()
         self._cleanup()
 
     def _process_packet(self, msg_type_proto: int, data: bytes) -> None: