Several things come to mind here.

CDO's are tough (I have done 2 years of them), but they are designed for you to sleep in the DAY, and be awake at night (hence still being on duty). So if you don't sleep in the day of course you will be tired. If you are stuck with a CDO schedule you must adapt (not easy) or change schedules (also not easy at some airlines).

My company uses very few CDO's now because our contract makes it VERY expensive for them. Other airlines can do the same.