Improving Operations in a Small Helpdesk System?

El Presidente asks: "I'm the department head of a small IT helpdesk in a not-quite-so-small business. The department's small in the sense that (a) there's only three people (including me), and (b) not only do we do helpdesk, but develop all the in-house systems, build our own servers, and more. We're supposed to log every helpdesk call that comes in (we've previously developed our own software for this), log notes on each call, and log the resolution. However, although I do set a good example by logging (most!) of my calls, the other two don't, even though I've asked them to do so numerous times. Although they do the job well, this is the one area that is letting the department down, and now management wants full stats on what we do every day, so obviously a full helpdesk log for each day would go a long way to prove what we do (or don't do). I don't want to come down on them with the Big Iron Fist (tm) and check up on them every few minutes, because I've got my own work to do. How can I actually get them to buy into logging calls, and not 'forget' or be 'too busy' to log things properly?"