Booked through Alamo many many months ago and just checked the site to see if the price has changed and if I was just booking now I would be paying almost $100 more for the week I have it booked (Nov 3rd). When I initially booked, anything between 3 and 7 days ws all the same price so we went for the week since the 4 extra days were bonus. I since got a code and addes to get it bumped from economy to compact ... even better.
Lesson being that not only can you rebook if you find a better rate, you may be lucky and have locked in a deal you won't get later.