Some comments on this debate.
There is a difference between short term tiredness and long term fatigue. Both can be hazardous with respect to safe flight. I would suggest that continual bad rostering can have an adverse effect on long term fatigue.
Far better that in flight rest be conducted in a pro-active manner- eg Captain says he is going to close his eyes for "x" minutes and to please wake me up at "y" time. Then FO can do the same etc. This is more effective than all on the flight deck trying to stay awake and then someone nods off in the process. When I was on the B707 in the 70's with (dare I say it!) BOAC, as a young Second Officer, I well remember on a night Altantic crossing looking over to see the skipper asleep and then also noting that the flight engineer was also in the same state!
I think it should also be considered that the rest period prior to duty is not just for sleep but also (dare I say it) for some form of recreation. Human beings are not machines and cannot sleep to order, especially after a long duty period. Rest periods of 10 hours or so are, I believe, quite insufficient to enable the average pilot to recharge the batteries prior to a new duty and the idea of longer duty periods etc I find quite horrifying both as a pilot and a fare paying passenger. There obviously has to be some sensible give and take but I feel the time has come for crew members to start drawing lines in the sand in this respect.