My last few trips have been on KLM. I take the 11pm JFK-AMS flight, eat lunch downtown in AMS, then hop the 7pm AMS-TLV flight. On the way back the flight leaves TLV at about 5:30am, with a short connection in AMS and arriving back in NYC mid-afternoon. This is always in coach. I usually go this route (1) for the miles, and (2) b/c it's cheap.
Going to Isarel, I try to sleep on the overnight JFK-AMS flight, and try to nap a bit on the AMS-TLV flight. That flight arrives at TLV at about 1am, so I don't make it to J'lem until about 3 or 4am, at which point I sleep until 8 or 9am, then get up and just try my hardest to make it through the day and not sleep until well after sundown.
On the way back, I usually just stay up all night until it's time to go to the airport around 2 or 3am. Then I sleep on TLV-AMS, and a bit on the beginning of AMS-NYC so I arrive back in the US tired, but still able to function until bedtime.
I don't use pills, and I set my watch for the plane's destination as soon as I get on board, and don't ever do the math to calculate the time where I've been except when I need to make a phone call.