Whenever we have flown with our cats, we were told Delta has a limit of 2 carriers first class cabin for some reason. It is my understanding depending on the aircraft there is a limit of 2 to 4 carriers in coach. I have no idea as to why Delta has a limit on pets seeing they charge such an absurd fee to bring a pet on board and it counts as one of your carryons. Be warned that Delta counts the carrier as one of your carryons even though you are paying a lot of money to bring the cat or dog on board.
I am not sure what species of a pet you are carrying on, but if it's a cat or a small dog, I would recomend a heavy duty cloth carrier. It is easier to manage as far as getting under the seat and you will have easier access to your pet. Also make sure you aren't assigned a first row seat since the carrier will have to go under the seat in front of you.
When we have to fly with our cats we can get both of them in the carrier and only have to pay one fee, so that is something else to consider if it's two small pets you are flying with, they both just have to be the same species. Our cats are best friends and it's a lot less stressful on them to be together in the carrier, so even if Delta were to charge us for two pets I would still try to keep them together.
I would also talk to your vet if your pet is hyper about possible meds to sedate him. Fortunately both our cats are great about travelling but some pets get traumatized by it.