i've heard a lot about this, and i'll give a quick sum up, but the bulk of the real information about these alternate sleep schedules can be found here:
http://en.wikipedia.org/wiki/Polyphasic_sleep
essentially, you cut out some to all the useless sleep stages and skip strait to the good stuff: REM. one can do this by going through a rough adjustment period of two weeks to three months (in which the deprivation can discourage) but once adjusted it CAN work for some folks who don't operate monophasically, like most with insomnia! if you're brain does not support the normal circadian cycle of 24.2 hours (and most of us with brain chemistry issues obviously don't!), maybe dividing up your REM sleep throughout the day could solve the problem of feeling rested.
like i said, the adjustment is rough and scheduling around everybody else who operates on a mono/biphasic sleep schedule can become a nightmare. i effectively operate on an Everyman 2 schedule (core nap of 3-5 hours and two 1- 1 1/2 hour naps) and function just fine on 4-7 hours of divided sleep a day (that is when i'm not manic, that throws the whole thing off for weeks!). you gotta be rigorous in timing these naps with only a 20-30 minute window of variation day to day, especially at first.
hope this might help some of you who are desperate for some of that precious REM!!