I don't know about the deli part, but we went to the little outdoor area that is tucked underneath another restaurant. It is a nice open air space with a few tables and a musician playing music. We only knew it was there because when we ate dinner at Alonzo's and the oysters were ridiculously priced at $2 and $3 a piece, the server told us about the 50 cent oysters at White Tarpon. She acted like she was hush hush about telling us, but turns out, the same person/company owns both restaurants. So we actually went to eat oysters after dinner instead of before. They were awesome! Very nice size and plentiful. There is a guy shucking them right behind the bar, so they are so fresh! We enjoyed them so much that we went back two more times during the weekend. It is our new favorite, can't go to Key West without going there, place!