diff --git a/telethon/client/dialogs.py b/telethon/client/dialogs.py
index 58a28d6f..9a209ec2 100644
--- a/telethon/client/dialogs.py
+++ b/telethon/client/dialogs.py
@@ -103,15 +103,27 @@ class _DialogsIter(RequestIter):
 
 
 class _DraftsIter(RequestIter):
-    async def _init(self, **kwargs):
-        r = await self.client(functions.messages.GetAllDraftsRequest())
+    async def _init(self, entities, **kwargs):
+        if not entities:
+            r = await self.client(functions.messages.GetAllDraftsRequest())
+            items = r.updates
+        else:
+            peers = []
+            for entity in entities:
+                peers.append(types.InputDialogPeer(
+                    await self.client.get_input_entity(entity)))
+
+            r = await self.client(functions.messages.GetPeerDialogsRequest(peers))
+            items = r.dialogs
 
         # TODO Maybe there should be a helper method for this?
         entities = {utils.get_peer_id(x): x
                     for x in itertools.chain(r.users, r.chats)}
 
-        self.buffer.extend(custom.Draft._from_update(self.client, u, entities)
-                           for u in r.updates)
+        self.buffer.extend(
+            custom.Draft(self.client, entities[utils.get_peer_id(d.peer)], d.draft)
+            for d in items
+        )
 
     async def _load_next_chunk(self):
         return []
@@ -236,12 +248,20 @@ class DialogMethods:
         """
         return await self.iter_dialogs(*args, **kwargs).collect()
 
-    def iter_drafts(self: 'TelegramClient') -> _DraftsIter:
+    def iter_drafts(
+            self: 'TelegramClient',
+            entity: 'hints.EntitiesLike' = None
+    ) -> _DraftsIter:
         """
-        Iterator over all open draft messages.
+        Iterator over draft messages.
 
         The order is unspecified.
 
+        Arguments
+            entity (`hints.EntitiesLike`, optional):
+                The entity or entities for which to fetch the draft messages.
+                If left unspecified, all draft messages will be returned.
+
         Yields
             Instances of `Draft <telethon.tl.custom.draft.Draft>`.
 
@@ -251,11 +271,21 @@ class DialogMethods:
                 # Clear all drafts
                 for draft in client.get_drafts():
                     draft.delete()
-        """
-        # TODO Passing a limit here makes no sense
-        return _DraftsIter(self, None)
 
-    async def get_drafts(self: 'TelegramClient') -> 'hints.TotalList':
+                # Getting the drafts with 'bot1' and 'bot2'
+                for draft in client.iter_drafts(['bot1', 'bot2']):
+                    print(draft.text)
+        """
+        if entity and not utils.is_list_like(entity):
+            entity = (entity,)
+
+        # TODO Passing a limit here makes no sense
+        return _DraftsIter(self, None, entities=entity)
+
+    async def get_drafts(
+            self: 'TelegramClient',
+            entity: 'hints.EntitiesLike' = None
+    ) -> 'hints.TotalList':
         """
         Same as `iter_drafts()`, but returns a list instead.
 
@@ -265,8 +295,16 @@ class DialogMethods:
                 # Get drafts, print the text of the first
                 drafts = client.get_drafts()
                 print(drafts[0].text)
+
+                # Get the draft in your chat
+                draft = client.get_drafts('me')
+                print(drafts.text)
         """
-        return await self.iter_drafts().collect()
+        items = await self.iter_drafts(entity).collect()
+        if not entity or utils.is_list_like(entity):
+            return items
+        else:
+            return items[0]
 
     async def edit_folder(
             self: 'TelegramClient',
diff --git a/telethon/tl/custom/dialog.py b/telethon/tl/custom/dialog.py
index c434e12e..b71b4c3f 100644
--- a/telethon/tl/custom/dialog.py
+++ b/telethon/tl/custom/dialog.py
@@ -87,7 +87,7 @@ class Dialog:
         self.unread_count = dialog.unread_count
         self.unread_mentions_count = dialog.unread_mentions_count
 
-        self.draft = Draft._from_dialog(client, self)
+        self.draft = Draft(client, self.entity, self.dialog.draft)
 
         self.is_user = isinstance(self.entity, types.User)
         self.is_group = (
diff --git a/telethon/tl/custom/draft.py b/telethon/tl/custom/draft.py
index 84289c58..a44986b7 100644
--- a/telethon/tl/custom/draft.py
+++ b/telethon/tl/custom/draft.py
@@ -2,10 +2,10 @@ import datetime
 
 from .. import TLObject
 from ..functions.messages import SaveDraftRequest
-from ..types import UpdateDraftMessage, DraftMessage
+from ..types import DraftMessage
 from ...errors import RPCError
 from ...extensions import markdown
-from ...utils import get_peer_id, get_input_peer
+from ...utils import get_input_peer, get_peer
 
 
 class Draft:
@@ -24,9 +24,9 @@ class Draft:
         reply_to_msg_id (`int`):
             The message ID that the draft will reply to.
     """
-    def __init__(self, client, peer, draft, entity):
+    def __init__(self, client, entity, draft):
         self._client = client
-        self._peer = peer
+        self._peer = get_peer(entity)
         self._entity = entity
         self._input_entity = get_input_peer(entity) if entity else None
 
@@ -39,17 +39,6 @@ class Draft:
         self.link_preview = not draft.no_webpage
         self.reply_to_msg_id = draft.reply_to_msg_id
 
-    @classmethod
-    def _from_dialog(cls, client, dialog):
-        return cls(client=client, peer=dialog.dialog.peer,
-                   draft=dialog.dialog.draft, entity=dialog.entity)
-
-    @classmethod
-    def _from_update(cls, client, update, entities):
-        assert isinstance(update, UpdateDraftMessage)
-        return cls(client=client, peer=update.peer, draft=update.draft,
-                   entity=entities.get(get_peer_id(update.peer)))
-
     @property
     def entity(self):
         """