I find that taking the minimal amount make a big difference here, and it's about 3 micro-grams (not milli-grams) for me. The trick is to get some liquid melatonin drops. There is a brand that has 3 milligrams per 30 drops as a recommended dosage, so I just take 3 or so drops and let them dissolve on my tongue. Using liquid drops this way, there is less of a sleep hangover, and It workes faster that way, too.
I think I read about 3 micrograms as more appropriate for most people on lesswrong, but it might have been somewhere else. It's working really well for me, with frequent breaks from it, for five or more years.