At one point in my career, I had 24-hour pager duty for a week as part of a time. I swapped someone else's Sunday morning for a Friday night and both of us were happy. Our bosses only cared that the time was covered. But, of course, not all managers are that flexible.Oh, and in case you are wondering, I want Sunday mornings so I can go to church services.
And I have to write that scheduling someone to shifts like your where you get over-tired is a recipe for less productivity at the very least. Maybe sometimes there's a special situation, but not as any sort of regular occurrence.