This approach is described by Eliezer Yudkowsky (http://en.wikipedia.org/wiki/Eliezer_Yudkowsky), a fellow probably best known for his Harry Potter pastiche Harry Potter and the Methods of Rationality (http://hpmor.com/). HPMoR is sometimes hilarious, sometimes ploddingly pedantic, sometimes horrifying. (You know how J.K. Rowling killed a significant character at the end of Book 4? Yudkowsky does a lot worse in Harry's first year.)
In HPMoR, Harry suffers from an interesting sleep affliction (http://hpmor.com/chapter/2):
In real life, Yudkowsky says he has a sleep cycle "around 24 hours and 30 minutes long ... my sleep cycle [advances] 3 hours per week (until my bedtime was after sunrise, whereupon I would lose several days to staying awake until sunset, after which my sleep cycle began slowly advancing again).""My sleep cycle is twenty-six hours long, I always go to sleep two hours later, every day. I can't fall asleep any earlier than that, and then the next day I go to sleep two hours later than that. 10PM, 12AM, 2AM, 4AM, until it goes around the clock. Even if I try to wake up early, it makes no difference and I'm a wreck that whole day."
Yudkowsky closes his latest Author's Note (http://hpmor.com/notes/98/) by describing how he commissioned:
(bowdlerism in original)... a long summary of extant research on non-24 sleep disorder, which I skimmed, and concluded by saying that -- based on how the nadir of body temperature varies for people with non-24 sleep disorder and what this implied about my circadian rhythm -- their best suggestion, although it had little or no clinical backing, was that I should take my low-dose melatonin 5-7 hours before bedtime, instead of 1-2 hours, a recommendation which I’d never heard anywhere before. And it worked. I can’t *#&$ing believe that #*$%ing worked.
(The original has Yudkowsky's Amazon affiliate links for three different brands of melatonin.)Currently I’m taking 0.2mg 5.5hr in advance, and taking 1mg timed-release just before closing my eyes to sleep. However, I worked up to that over time – I started out just taking 0.3mg total, and I would recommend to anyone else that they start at 0.2mg.
I don't recommend HPMoR (or recommend against it). I don't recommend melatonin (or recommend against it, though it didn't overall work for me when I took it many years ago). I know absolutely nothing about the group Yudkowsky turned to. Please do your own research.
I have no idea how this might work for others, but I thought this knowing about this approach might inform members of this forum.