Delta seems particularly annoying about it because they don't publish the underseat dimension restrictions. The specifics will depend on your aircraft, but I've been flying with these carriers: on Alaska without any problems. The published dimensions are slightly larger than the limits Alaska lists, but the carrier is squishable, so it fits easily under the seats in both their 737s and ERJ-175s (the RJs have more space!). I suspect it will similarly fit underseat on any mainline and larger RJ Delta aircraft. It's safer to use a soft carrier than a hard one because of protrusions into the nominal underseat space that the airline might ignore in the dimension listings.

One thing to watch out for is that the underseat space for the aisle seats tends to be smaller than for middle and window, and in some aircraft there can be an IFE box taking up some of that space, so I stay away from aisle seats when flying with a pet.