Every carrier has their own rules. This is what Airtran says on their site:

Traveling with a Pet
Small, domesticated cats, dogs and birds that will fit in an approved carrier under the seat are accepted.

The pet kennel is limited to maximum dimensions of 8.5" high x 17" long x 12" wide.
The carrier must be leak proof and ventilated on at least two sides.
There is no weight restriction on pets.
The pet must remain in the carrier and under the seat for the duration of the flight.
The pet carrier counts as either a passenger's one (1) carry-on bag or personal item.

Airfare for a pet is $69 one-way and is non-refundable. Six (6) pets are allowed per flight with a limit of one (1) pet per paying customer traveling on the same flight.

As limited space is available, advanced reservations must be made. Of course, service animals (e.g., Seeing Eye dogs) are always welcome onboard regardless of the number of pets already booked on the flight.

I own the medium size Sherpa ULTIMATE PET CARRIER and have used it for years traveling with my Cavalier King Charles Spanel. The bag's specifications are 17" D x 11" W x 10.5" H, Weight: 3.09 lbs.. Their large bag is 19" D x 11.75" W x 11.5" H, Weight: 3.45 lbs. I have never had a problem using this bag on any carrier. That being said, my Cavalier only weighs 12 pounds so needless to say the bag is comfortable for her.

You must also remember that the beauty of these soft sided pet carriers is that they are flexible and can be pushed under the seat. That is why you will find many posts in this forum stating that if it is an inch or two larger that the airline's specifications you shouldn't worry.