I have used Cheaptickets and always check them when buying a ticket on my own dime. Twice I got about 10% savings ($20 on $211) on IAH-SLC on CO nonstops. I chose the times and compared the prices and got my miles. Just open two browser windows and have Cheaptickets and some other service (I use ITN) price the seats at the same time.
Usually there are the best discounts on TW and AWA. But know this, the change fee is supposed to be $150 on the tickets and they are not upgradeable. (That said, I changed one reservation for $75 and got upgraded on another.)

The uncertainty of airline and time on Priceline.com is what keeps me away.

BSL