Check for offbrand car rental companies. My dad swears by two of them, but unfortunately I'm blanking on the name. He uses them for business rentals (consulting, not reimbursed) when he travels. I think Fox is one of them.
Also, consider Priceline's bid option. Once you've located the cheapest option via regular means, go on Priceline and bid 15% less. It's been a while since I bid on Priceline (and I never did rental cars), but it used to be that you could re-bid immediately as long as you changed a detail (like adding another departure airport or shifting your dates a bit), so you could hopefully try again if the first bid was rejected. Also, there used to be websites that listed recent successful bids so with some research, one could have a pretty good idea of what would be accepted. The Priceline site itself allows you to see recent winning bids. Raleigh shows bids at #20, $23, $24, $28, and $30 (as the low end) per day. It doesn't give the dates or lengths, but it's a place to start.