Never mind 1,000 words or fewer--how about 50 words, 30 words, 25 words or fewer for a short story?
Author and anthologist Robert Swartwood has coined hint fiction as an ultra-short fiction--25 words or fewer, as a matter of fact.
In his article at Flash Fiction Chronicles (linked above) he states:
Me, I want to coin a term, so I’m going to do it here and now: those very, very, very, VERY short stories should be called Hint Fiction. Because that’s all the reader is ever given. Just a hint. Not a scene, or a setting, or even a character sketch. They are given a hint, nothing more, and are asked — nay, forced — to fill in the blanks. And believe me, there are a lot of blanks.He is the editor for the anthology Hint Fiction: An Anthology of Stories in 25 Words or Fewer, published by W.W. Norton and Co. From the publishers webpage blurb:
A story collection that proves less is more.
The stories in this collection run the gamut from playful to tragic, conservative to experimental, but they all have one thing in common: they are no more than 25 words long. Robert Swartwood was inspired by Ernest Hemingway's possibly apocryphal six-word story—"For Sale: baby shoes, never worn"—to foster the writing of these incredibly short-short stories. He termed them "hint fiction" because the few chosen words suggest a larger, more complex chain of events. Spare and evocative, these stories prove that a brilliantly honed narrative can be as startling and powerful as a story of traditional length. The 125 gemlike stories in this collection come from such best-selling and award-winning authors as Joyce Carol Oates, Ha Jin, Peter Straub, and James Frey, as well as emerging writers.Swartwood will be the judge for a hint fiction contest, too, sponsored by Smokelong Quarterly. Celebrating their 30th issue, the SQ will choose the perfect hint fiction of exactly 30 words--so submit during the thirty days of November.