It really depends on what you mean by small.
Also, in almost every situation - shipping is a weight/destination charge - and the smallness of the box has nothing to do with it.
2 lbs coast to coast is $12.75 Priority or $12.21 Ground even for a small box. You have not told us the size or the weight of the shipment.
The only other options are flat rate boxes - and the small flat rate box costs $7 regardless of weight/destination and is about the size of a VHS tape.
Unless the package qualifies for media mail or first class mail, the price likely isn't going to be cheaper
