I always do this, and while about 80% of the time the prices are equal to or higher than what I'm reserved at, quite often (particularly on weekend stays) the price is lower!

In such case, I immediately reserve at the lower rate, then cancel the older reservation at the higher rate. (Always do it in that order, don't take your foot off the first reservation until you're safely on the lower rate, because sometimes it's a mistake and then you may be unable to get your earlier rate back.)