Having worked on, and used, helpdesks I know that the checklist system many use needs to be developed properly. The idea is to have a good, strict, method both for reporting problems and for resolving them through the traditional ticket model.

A good overview of how to produce such a system through this piece. Getting the system right will make a big difference to the efficiency of your ticket system and you resolve the issues, and should make a difference to your staffing levels to, if he improvements make it easier to identify and resolve issues.