The latest research indicates that sleep is the critical variable. Try not to set off on a trip with a sleep deficit--getting a few hours of extra sleep the night before can help.
When I go east-to Europe, I take a mild sleeping pill, and get about 4 hours. I then go to bed early, if possible, and sleep for as long as possible--sometimes 10 hours. I get up the next morning, and carry on normally. It's the best I've discovered, almost no jet-lag, perhaps a bit slow the first two days or so, but not groggy or headachy. The idea is that if you have enough sleep, the 'clock' will reset itself. Works for me.