I've also learned that fans come in various strengths in terms of how much air they move - and for reasons I won't get into here I'm going to get the "Tornado" version if they make such a thing.
EDIT: New fan is in, 30% more fan capacity than the previous one. New one also includes a light, which the old one didn't have. As there previously had been no light, there is no separate light switch, and the fan & light therefore switch on and off as a unit.
In the process of doing this, all sorts of filth rained down into the bathroom, so before I clean myself up I have to do an unscheduled cleaning of the room below the work site. Really I should have figured that was going to happen.