Here's another strategy...

If I have a Tuesday 0300 launch, I stay up as late as I can on Sunday night, until say, 0300 or 0400. Then I go to sleep in my own bed, and sleep as late as I can, say, noon or 1300. I go to the airport to catch my jumpseat, sleep on the way to MEM, take a 1-2 hour nap at midnight between my jumpseat and my trip, and I am good to go.

By staying up Sunday night, I am transferring the "first night" syndrome from the night I fly, to the night I am getting ready to go to work.

Technique only, but it works for me.

For the most part, night flying gives you longer time in the hotel. Day flying gives your shorter layovers, and longer time in MEM. I find that I get more sleep by flying at night, as I can't always force myself to sleep in order to get my 8 hours before my 0430 wakeup for my day flight.

Again, that's just me.

If I could be in charge for one day, I would ban all 24 hour layovers that launch in the am. You can't get good sleep twice in 24 hours, and the constant switching back and forth of your body clock wears you out. IMHO, it is just as fatigue inducing as an international trip that changes a bunch of time zones.