After lots of checking we found by far the best deal for Enterprise through Travelocity. Read on...I had some successes with a discount and upgrade.
While rate-shopping we checked the rental car sites, Costco, Travelocity, Orbitz, Expedia, Interval International, and the airline frequent flier sites. Then we checked discount codes from AAA, AARP, public TV membership, Interal International, and several professional organizations, plugging them in to the various sites above. Most of those codes were for larger cars, and we wanted the least expensive. Finally we reserved an economy car with Enterprise through Travelocity.
At the airport rental car center (Phoenix), the lines for Enterprise were very long, and virtually nobody was at any of the other counters. I went to the nearby counters and asked if they'd match the price, but no deal.
Once we got to the front of the Enterprise line, I mentioned AAA and the agent zapped another 10% off what was already the best rate. When we got the car, it was unsatisfactory - the driver's seat was too cramped, and the seat belt buckle poked my hip. We asked for a substitute, and they gave us a car that smelled. We asked again, and they gave us an upgrade to a very nice car that would have cost more. The agent told us that as it gets later in the day and they run out of the smaller cars, they automatically upgrade to better ones, and then when they run out of cars entirely they pay for people to get cars from the other agencies. All this took some time, so I commented that we shouldn't have to pay for extra hours that were on the initial contract - those got zapped off as well.
Bottom line - saving $10-$20 wouldn't have been worth the hassle, but not settling for an unsatisfactory car yielded us a nice upgrade at no cost.