On mine, the delicate cycle does not spin as fast as the regular cycles. I think this may be typical of delicate cycles on front loaders. What brand and model do you have? It would help to get feedback from people who have your specific machine. (Mine is a 10-year-old Asko, which not many people would have.)
Edit: Should add, though, that I have not had water remaining for my delicate cycle runs. On the other hand, I don't think I have ever run t-shirts through the delicate cycle; have run a sweater at a time through, though, and still no water remaining.