Even if it doesn't end up helping, its cheap enough, and certainly harmless enough stuff.
Never tried it in practice, but from what I've read on the SAR of melatonin itself in TIHKAL (alexander&ann shulgin), melatonin is actually quite a decent radioprotective agent, helping resist the effects of radioactive exposure. I do wonder if oxidative stress, from long haul flights might have something to do with the feeling scrappy, after absorption of greater than normal background radiation due to the high altitude could play some part in jet-lag. Next time I have cause to fly, I think I'll try pro-loading the couple of nights pre-flight, take a further dose, or two during the flight itself, depending upon its duration, and continue for a further 2-3 days after, to help reset my circadian rhythms (hah! as if I had one to begin with:P)
Along with plenty of food/drink high in antioxidants, lots of fresh fruit juice, not the processed, reconstituted stuff, but I LOVE fresh grapefruit juice, with the pulp and bits in it, fresh orange, or fresh pomegranate juice. My favourite of all though, I think, have to be either guava, or mango juice. The grapefruit juice can interact, in large quantities, with certain meds though, raising or decreasing plasma levels depending upon the medication in question. Packed full of vitamin C, and antioxidant flavonoid compounds.