diff --git a/telethon/tl/custom/conversation.py b/telethon/tl/custom/conversation.py
index 2f91cda1..f6b69cd9 100644
--- a/telethon/tl/custom/conversation.py
+++ b/telethon/tl/custom/conversation.py
@@ -138,7 +138,7 @@ class Conversation(ChatGetter):
             lambda x, y: x.reply_to_msg_id == y
         )
 
-    async def _get_message(
+    def _get_message(
             self, target_message, indices, pending, timeout, condition):
         """
         Gets the next desired message under the desired condition.
@@ -192,11 +192,12 @@ class Conversation(ChatGetter):
                 return future
 
         # Otherwise the next incoming response will be the one to use
+        #
+        # Note how we fill "pending" before giving control back to the
+        # event loop through "await". We want to register it as soon as
+        # possible, since any other task switch may arrive with the result.
         pending[target_id] = future
-        try:
-            return await self._get_result(future, start_time, timeout)
-        finally:
-            pending.pop(target_id, None)
+        return self._get_result(future, start_time, timeout, pending, target_id)
 
     async def get_edit(self, message=None, *, timeout=None):
         """
@@ -222,12 +223,9 @@ class Conversation(ChatGetter):
             return earliest_edit
 
         # Otherwise the next incoming response will be the one to use
-        future = asyncio.Future(loop=self._client.loop)
+        future = self._client.loop.create_future()
         self._pending_edits[target_id] = future
-        try:
-            return await self._get_result(future, start_time, timeout)
-        finally:
-            self._pending_edits.pop(target_id, None)
+        return await self._get_result(future, start_time, timeout, self._pending_edits, target_id)
 
     async def wait_read(self, message=None, *, timeout=None):
         """
@@ -246,10 +244,7 @@ class Conversation(ChatGetter):
             return
 
         self._pending_reads[target_id] = future
-        try:
-            return await self._get_result(future, start_time, timeout)
-        finally:
-            self._pending_reads.pop(target_id, None)
+        return await self._get_result(future, start_time, timeout, self._pending_reads, target_id)
 
     async def wait_event(self, event, *, timeout=None):
         """
@@ -284,20 +279,9 @@ class Conversation(ChatGetter):
         counter = Conversation._custom_counter
         Conversation._custom_counter += 1
 
-        future = asyncio.Future(loop=self._client.loop)
-
-        # We need the `async def` here because we want to block on the future
-        # from `_get_result` by using `await` on it. If we returned the future
-        # immediately we would `del` from `_custom` too early.
-
-        async def result():
-            try:
-                return await self._get_result(future, start_time, timeout)
-            finally:
-                del self._custom[counter]
-
+        future = self._client.loop.create_future()
         self._custom[counter] = (event, future)
-        return await result()
+        return await self._get_result(future, start_time, timeout, self._custom, counter)
 
     async def _check_custom(self, built):
         for i, (ev, fut) in self._custom.items():
@@ -317,32 +301,23 @@ class Conversation(ChatGetter):
 
         self._incoming.append(response)
 
-        found = []
-        for msg_id in self._pending_responses:
-            found.append(msg_id)
+        # Note: we don't remove from pending here, that's done on get result
+        for msg_id, future in self._pending_responses.items():
             self._response_indices[msg_id] = len(self._incoming)
+            future.set_result(response)
 
-        for msg_id in found:
-            self._pending_responses.pop(msg_id).set_result(response)
-
-        found.clear()
-        for msg_id in self._pending_replies:
+        for msg_id, future in self._pending_replies.items():
             if msg_id == response.reply_to_msg_id:
-                found.append(msg_id)
                 self._reply_indices[msg_id] = len(self._incoming)
-
-        for msg_id in found:
-            self._pending_replies.pop(msg_id).set_result(response)
+                future.set_result(response)
 
     def _on_edit(self, message):
         message = message.message
         if message.chat_id != self.chat_id or message.out:
             return
 
-        found = []
-        for msg_id, pending in self._pending_edits.items():
+        for msg_id, future in self._pending_edits.items():
             if msg_id < message.id:
-                found.append(msg_id)
                 edit_ts = message.edit_date.timestamp()
 
                 # We compare <= because edit_ts resolution is always to
@@ -353,8 +328,7 @@ class Conversation(ChatGetter):
                 else:
                     self._edit_dates[msg_id] = message.edit_date.timestamp()
 
-        for msg_id in found:
-            self._pending_edits.pop(msg_id).set_result(message)
+                future.set_result(message)
 
     def _on_read(self, event):
         if event.chat_id != self.chat_id or event.inbox:
@@ -379,7 +353,7 @@ class Conversation(ChatGetter):
         else:
             raise ValueError('No message was sent previously')
 
-    def _get_result(self, future, start_time, timeout):
+    async def _get_result(self, future, start_time, timeout, pending, target_id):
         due = self._total_due
         if timeout is None:
             timeout = self._timeout
@@ -387,11 +361,14 @@ class Conversation(ChatGetter):
         if timeout is not None:
             due = min(due, start_time + timeout)
 
-        return asyncio.wait_for(
-            future,
-            timeout=None if due == float('inf') else due - time.time(),
-            loop=self._client.loop
-        )
+        try:
+            return await asyncio.wait_for(
+                future,
+                timeout=None if due == float('inf') else due - time.time(),
+                loop=self._client.loop
+            )
+        finally:
+            del pending[target_id]
 
     def _cancel_all(self, exception=None):
         for pending in itertools.chain(