How about a short short story?
I know Hemingway is said to have claimed that his best short story went like this: "For sale: baby shoes, never worn." While this seems to be a more or less truthful anecdote, this kind of strikingly short way of expression has spawned a movement of six word stories and other kinds of flash fiction. In Norway, a book called "Du trenger ikke mer enn 6" ("You don't need more than 6") has been published - no doubt inspired by the Hemingway-anecdote.
This really isn't my area of expertise, but I immediately thought of a short short story by Richard Brautigan, brilliantly named "The Scarlatti Tilt":
"'It's very hard to live in a studio apartment in San Jose with a man who's learning to play the violin.' That's what she told the police when she handed them the empty revolver."
And that's it!
It's perhaps not too difficult to write stories in a fragmental way which the reader has to put together to a kind of meaningful web, but more interesting, I find, to write short short stories with a point or plot. These kinds of stories share the structure with the riddle or joke, but are still something different.
A short short post on a long long Sunday.