Melatonin appears to be very effective. There is some good evidence to suggest this.
Please read - "Melatonin for the prevention and treatment of jet lag." by Herxheimer A, Petrie KJ.
"........Melatonin is remarkably effective in preventing or reducing jet-lag, and occasional short-term use appears to be safe. It should be recommended to adult travellers flying across five or more time zones, particularly in an easterly direction, and especially if they have experienced jet-lag on previous journeys. Travellers crossing 2-4 time zones can also use it if need be......."
Also read - "Sleep and intercontinental flights." by Nicholson AN
"........travellers must look after their sleep, as far as possible, during and after the flight. The most useful time for sleep during the flight must be anticipated, caution exercised in the use of hypnotics in-flight as reduced mobility is a potential risk factor for venous thrombosis, and a strategy adopted, whether flying east or west, to adapt as quickly as possible to the working hours of the new locality. After an eastward flight a hypnotic may be useful, but this strategy is seldom necessary after a westward flight unless the journey has involved crossing more than 5 or 6 time zones. The claim that melatonin accelerates the shift of the sleep-wakefulness cycle to a new time zone is controversial, and its recommended use may prejudice alertness during working hours. Exposure to artificial light and avoidance of ambient light at certain times of the day could prove to be of help-possibly in conjunction with drugs..............."