Upvote:12
Delta allows one "carry on bag" and one "personal item" on board. The carry on bag is allowed to go in the overhead bins, while the personal item must fit under the seat in front of you. So it is perfectly fine to bring one carry on bag and your laptop case as a separate personal item, as long as the laptop case fits under the seat (I've never seen one that doesn't) and you don't have any other personal item (purse, briefcase, etc.).