In all seriousness, I've seen mentions of studies that suggest going from 8 hours to 6 does _not_ correlate with a 25% decrease in productivity, because most people aren't consistently productive for all 8 hours of a day. I know in my case, there's an extremely strong inverse correlation with productivity and how bored I am with a particular task. I'm sure I'm not alone.
When I first started freelancing hourly, it was a sobering feeling to see how little of my time was actually billable for actual work. It takes random screen grabbing software to make you realize that most of the time you are not working. Of course those days have long passed for me but I’m always left to remember just how wasteful office workplaces are and how much time people waste away in their life. More than half of their working life is a total waste. Tell me, how does that make you feel? :)
Lack of sleep is very rarely an issue with your employer.