In our company it's ok to have a rest in the flight deck, simple rules, one pilot at the time, advise the back end and schedule a call no more than 45min after being advise just in case the second pilot dosed off. and wake up at least 20min before TOD...but on a short flight they must have been tired before leaving....
Anyways North America has to enforce stronger rules on duty days and ban continues duty, impose restrictions on red eyes and give better protections to pilots turning down flights because of fatigue.....ALPA where are you????
BZH
EX cargo driver....