Where I work there is a pretty complex bidding process for HP days, where every day is allocated a number of points directly proportional to how popular a date is.
The more points you have the less chances you have to get what you want the following year.
Not a seniority based at all, and it prevents the same people from getting the top summer periods and christmas every year.
Very fair in my opinion.
No chance to request days off on a fixed pattern.