Comp Time for Part Timers

My agency or, at least, my location, does not afford part-time employees the option of selecting comp-time for hours in excess of 8 per day or 40 per week. Is this difference between full-time and part-time employees permissible?

Overtime and Annual Leave

A nursing supervisor requests an RN (Registered Nurse) who is on annual leave to work overtime. The RN agrees to work a day during her annual leave for the overtime as promised by nursing supervisor. Can the nurse be paid overtime in this situation?