In February, Delta banned pets in the cabin in international business class. With the airline installing lie-flat seats in that section, space is limited for pet carriers under seats.
Late last year, after a string of deaths of bulldogs and similar breeds, Delta banned snub-nosed dogs and cats as checked baggage.
"Safety always has to be the top priority," said Delta spokesman Anthony Black.
Delta also will generally not carry pets as checked baggage from May 15 through Sept. 15, or anytime when the outside temperature is above 85 degrees or below 10 degrees at any point the plane is on the ground during the trip.
More than half of reported pet deaths on U.S. airlines last year were on Delta, according to federal data. But Delta said the number of pets that are injured or die on the airline is less than 0.2 percent of pets carried.
Last week, the U.S. Department of Transportation proposed new procedures, including: requiring reports of incidents involving not just pets but also cats and dogs shipped commercially, such as by breeders; requiring airlines to report how many animals they transport to compare rates of animal incidents between airlines; and requiring more airlines to report pet incidents. The DOT is taking public comments on the proposal until Aug. 28.
Southwest and AirTran Airways both allow crated pets in the cabin, but do not allow pets as checked baggage or cargo.
Those traveling with pets should check with their airline well in advance for current regulations, according to the American Veterinary Medical Association, adding that airlines sometimes update their restrictions on pet travel.
"If the airlines are making these decisions based in whole or in part on the health and welfare of the animal, then it's a good thing," said AVMA spokesman David Kirkpatrick. Before flying with pets, "owners need to do a good amount of research."