The shortest, wittiest, most formal poetry publication that I know of is Brooke Clark’s Tumblr-based Asses of Parnassus. This is the place for pieces as short as a couplet or perhaps a couple of quatrains, whether you are submitting for publication or you simply like reading them.
The irreverence is illustrated with the Tumblr heading: a detail of a Goya etching from his series of caprichos, morbid, satirical and anti-establishment in outlook.
The Asses of Parnassus used to contain a lot of translations (in rhyme) from Greek and Latin authors – lots of rude, snide, scurrilous comments from Martial and Catullus – but is now dominated by more current material. The most recent item as this post is being written is a 24-line screed from Daniel Galef on being denied a Wikipedia entry. The one before is my own couplet, Success:
“Success!” he toasted. Though I wished him dead
I smiled and raised my glass: “Suck cess!” I said.
But though rude and snide are allowed, you are unlikely to find any bigotry or hatred. Brooke Clark retains tolerance and even compassion in The Asses of Parnassus. He is Canadian, after all.