Yes they do exist, but as you would guess they are mostly during 'off peak' times. If you have some flexibility with dates you should be able to get a good deal. BUT if you are tied to school holidays you will be very lucky to pick up a really cheap deal.
Travelocity allow you to set up a Fare Watcher. You pick your destination airports and the price you want to pay and they e-mail you if/when it reaches or goes below that price.
If you are tied to school holidays, try looking as soon as the flights go on sale. I got a particularly good deal for Christmas from ebooks by booking as soon as the flights went on sale.
Flying indirect is usually cheaper, if you can put up with the longer travelling time. Other than that keep looking! Good Luck
Maxine