I've been training my own versatility horse, and to get his jog, I asked for a trot, and consistently slowed him up by doing half halts. When he was as slow as I wanted (and my 'slow' got slower and slower every ride) I praised him and walked him. Now he jogs almost instantly when I ask :) Lope is a little different, but I can't exactly say we have our lope down yet. I ask for a canter, and I slow him down by doing long half halts (almost 2 strides before I release) But you have to time when you release so he doesn't completely fall on his face. During the first stride of the half halt, he drops his head, the 2nd stride he slows down. Same with that, once you get to the 'slow' you want, praise him and walk him. Once I actually get the lope I want, I'll let you know any tricks I figure out ;)
Eventing: the only sport where you wear your medical information strapped to your arm.