Does anyone know if there is a cheaper rate for mailing books to the USA?

Cheaper than what? If you don't have a lot, just bring 'em to the post office. It' s dirt cheap, but will take at least a few months.

If you have a lot of stuff to send (maybe 50 or more kilos??), you can arrange for a tea chest with Seven Seas: www.sevenseasworldwide.com/