I’ve just found this site! http://www.short-stories.co.uk/
There are age recommendations for each story, plus an indication of story length, to help you find one at your level.
@Helen!
mmmmmmmmmmm!
Thanks! This seems good food for bookworms!
Thanks for posting this!
Thank you Helen. It looks very interesting! I’ve added it to my list of interesting resources 
Thanks, Helen! I think I’ll use those stories with my students, though, as I don’t have that much time to read it all by myself
I conducted an experiment with some Russian students the other week. I found the text of “the Three Little Pigs and the Big Bad Wolf” on the internet and got them to read it, then retell the story. The pre-intermediate found it very hard, the intermediate found it an interesting challenge, the upper-intermediate seemed to really enjoy it and the advanced student found it quite easy.
Since then (as a result or not, I don’t know) the pre-intermediate and the intermediate have started reading English graded readers, and they say that they enjoy English lessons much more now than they used to. We base vocabulary, grammar and pronunciation work on the story they are currently reading, rather than working through a textbook (which neither of them showed much enthusiasm for).
Make of that what you will, but I think there’s certainly a place for short stories in the classroom, even among students who swear blind that they are too busy for such time-wasting friviolity.
@skyblueteapot
It is very interesting and useful site. Thanks!