Twice recently I've shipped bikes from a few states away with UPS/BikeFlights. There is a size cutoff that made the price jump from $60 to $160. Playing with the shipping calculator, here are the limits to stay at the lower price threshold:
54 x 8 x 30
54 x 9 x 28
56 x 9 x 28
55 x 8 x 29
52 x 9 x 30

There is also some art to the order process - if the box is 8.5" wide, and you need it to be 8" - use 8". No one at UPS is going to check.

I recently shipped a road bike with a 53 ctt seat tube, and it fit a box under the limit easily. Select the right box or cut it down.