During a chat about the pros and cons of gmail, a colleague told me that he especially likes how gmail inserts your sent messages into the same thread as the one you're replying to.
The idea that a webmailer should be more useable than my beloved mutt simply didn't fit my view of the world. I'm allergic to webmail.
A bit of web search soon brought me this nugget for insertion into my .muttrc:
set record = "^"
Got it from here, and it works like a charm. You'll need mutt version > 1.5.10 or the current_folders patch.
I'm probably the last person on earth to find out about this.
Bye bye, "sent" folder.