So I've been to Dempsey's a few times now, twice for lunch and once with a group of six for dinner and I think it warrants a CH mention. The place itself is--I swear-- larger on the inside than on the outside, I don't know how they do that. We wandered in on Friday at 7 and were seated promptly. Judging from the activity at lunchtime I figure the place has a steady stream of patrons more than an overwhelming crush at proper dining out times.
There were some real standouts: the oysters were excellent--firm, slightly briny, nicely shucked--and cheap money (priced at $9/dozen but there were 15 on the plate). The stuffed artichoke was indeed a stuffed artichoke, I'd never encountered anything quite like that before. The stuffing was nicely seasoned and not, as can be the case with stuffings, too salty. The frogs' legs were plump and juicy; the "blackened" redfish was fresh, appropriately seasoned, and not cooked to death. A friend with some dietary restrictions had grilled shrimp minus the cheese sauce. Frankly I think the sauce would have been paint on the lily: there was enough flavor (and enough shrimp!) on that plate to stand on its own. And you've heard about the mac & cheese, right?
The fried seafood platter (nominally for two) was really too much food for four. They do a good job with the frying, it tastes clean and isn't greasy but ordering this was a kind of one off thing, there's only so much fried catfish a person can eat. Mind you, the little fried up balls of goodness were pretty excellent though and the seafood gumbo was solid if not outstanding.
All of that plus the kind of service you remember from the neighborhood joint when you were a kid: competent waitresses that you're just a little scared of.
A couple of random notes: they'll do 1/2 sized apps, the onion rings and fries are only okay, and--maybe most delightfully of all--they serve draft Abita in large schooners, nay, chalices.
At any rate, it's not fine dining and it's not very cheap but I'd recommend it.