Advance purchase prices seem to vary more at LAX than at most airports. When you try to reserve more than six weeks in advance, you may pay two or three times as much as if you check the SAME company's website three or four weeks ahead. Book ahead, and keep checking back. When the price drops, cancel the older res. Lather. Rinse. Repeat.

And I've had good luck lately with Dollar. Thrifty, not so much. Go figure.