This is exactly what I do. *I book the new one, cancel the old one. I make sure to keep a printed copy of all of the cancellations in case there is a question. I did it with National a dozen times at least on my last trip.
This is the one part of travel where you can cancel and rebook. Air is basically done once you buy it.
I always re-book, then cancel. That way, if I can't get the new, better rate for some reason, I still have the old, still-pretty-good rate to fall back on.
National has a great area on their site where you can modify. You put inb your new codes and see if that gets you a better rate. they put the old rate and the new next to each other. Then you either click take new rate or stay with old.
I have modified 3 times already, once to a different pick up site. I got an e-mail with each change to let me know the new rate has gone through. this past time when I changed the pick up site they changed the ressie confirmation # and pointed it out at the top of the e-mail. I went from having the car for 3 days at a rate of $187 to having the car for 7 days at a rate of $120.
I really love National and since I get such good rates I haven't even looked at any other.
I used to get the best rate possible from any agency then go to L&M and ask them to match. They always matched rates so I got a good rate from an on site agency. but with the National Emerald Club it is fun to pick out whatever I feel like driving.
I always book and cancel...but I love to check the National Itinieries in Emerald Club....it is great if you are afraid you are missing or forgot to cancel a ressie.