1-3 hours? Do you have a source for that advice? Everything I've read, and my personal experience with it, suggests taking it (as you say, .5 to 1mg) 30 minutes before you want to fall asleep.
http://www.talkaboutsleep.com/how-to-use-melatonin-correctly...
Number of hours are all over the map. Hey, if you feel its effects within 30 minutes, then that's what you should use...