diff --git a/telethon/events/callbackquery.py b/telethon/events/callbackquery.py
index 886cca14..142a9d5a 100644
--- a/telethon/events/callbackquery.py
+++ b/telethon/events/callbackquery.py
@@ -235,6 +235,12 @@ class CallbackQuery(EventBuilder):
             Returns the edited :tl:`Message`.
 
             This method also creates a task to `answer` the callback.
+
+            .. note::
+
+                This method won't respect the previous message unlike
+                `Message.edit <telethon.tl.custom.message.Message.edit>`,
+                since the message object is normally not present.
             """
             self._client.loop.create_task(self.answer())
             return await self._client.edit_message(
diff --git a/telethon/tl/custom/message.py b/telethon/tl/custom/message.py
index c980857c..7a632ba2 100644
--- a/telethon/tl/custom/message.py
+++ b/telethon/tl/custom/message.py
@@ -628,10 +628,28 @@ class Message(ChatGetter, SenderGetter, TLObject, abc.ABC):
 
         Returns ``None`` if the message was incoming,
         or the edited `Message` otherwise.
+
+        .. note::
+
+            This is different from `client.edit_message
+            <telethon.client.messages.MessageMethods.edit_message>`
+            and **will respect** the previous state of the message.
+            For example, if the message didn't have a link preview,
+            the edit won't add one by default, and you should force
+            it by setting it to ``True`` if you want it.
+
+            This is generally the most desired and convenient behaviour,
+            and will work for link previews and message buttons.
         """
         if self.fwd_from or not self.out:
             return None  # We assume self.out was patched for our chat
 
+        if 'link_preview' not in kwargs:
+            kwargs['link_preview'] = bool(self.web_preview)
+
+        if 'buttons' not in kwargs:
+            kwargs['buttons'] = self.buttons
+
         return await self._client.edit_message(
             await self.get_input_chat(), self.id,
             *args, **kwargs