Try a mom-and-pop used car shop. Their underage fees will be less or nonexistent. You will most likely have to deal with: no one-way rentals, older junk, geographic restrictions on mileage, mileage caps or show your airline pass to get free unlimited miles, a letter from your insurance company saying you have liability insurance and don't need to purchase their expensive one, etc.
Avis used to not allow underage rentals, period. Hertz and Budget did, for a high price, and now Hertz has a coupon to waive the fee for weekly rentals, so Avis lately decided to match them. Alamo has a smaller underage fee, typically an extra $9-$15/day. Enterprise, which was conceived to compete with the mom-and-pops, allows underage renters to add the charge when they book their reservation.
Many corporate contracts waive the underage fees, and can be used for both business and personal travel. (Personal travel doesn't cost the company a dime, and the rental company gets more business.) Inquire with your corporate travel department.
Regardless of whom you book with, underage renters are typically not allowed to drive large specialty vehicles, like minivans and SUVs. I suggest calling before you reserve something only to be turned away at the counter.