What I have found to be the cheapest for me is to fly delta direct to London and then take a flight from london to limmasol (sp?). As far as price goes I think the flight from london to cyprus was around 400? and the delta to london non stop just around 800. This is probably what I will do, and I wouldn't mind paying more as long as the flight is direct without a really long layover. If I find a better option I'll post it.