I just discovered this one with a week left to go before the deadline!
Now in its 15th year, this contest held by Carve Magazine is accepting submissions. They offer a $1,500 (!) prize to the winner. Submissions are due (postmarked/emailed) by May 15th.
There is an entry fee for this one: $17 online/ $15 mailed. For full details, visit the rules page at Carve Magazine.
For regular fiction submissions, visit their writer’s guideline page.