How do you handle annual leave requests during winter pressures?

We're a 4-partner practice with 18 staff. Every December I end up in the same fight — half the team want Christmas week off and I can't refuse everyone. What AL policies do other practices use? We currently run a first-come-first-served approach but it feels unfair to staff who plan later. Is there a better way? Thinking about moving to a ballot system or a rota but partners aren't keen on the admin.