While for years I have used the two BFH method which gives a level of satisfaction that is hard to describe, due to the limited space to take a good swing under a Mini guard, I also have one very similar to phillb's picture.
My advice is to get a reasonable quality one, as it will tend to be thinner where it slides between the ball joint rubber seal and the suspension or steering arm and usually a little less 'bulky' making it easier to get in where it needs to be. Mini stuff is quite a bit smaller that what is generally found on full size cars, so many of the ball joint splitters are too wide in the jaw. Also, as soon as I got it I pulled it apart and greased the pivot pin, bolt thread and where the bolt rides on the arm with a good quality grease.
I can tell you first hand that the cheap bulky ones with wide jaws, when used on Mini tie rod ends for instance, are very hard to load evenly and because of the cheap material (which is why they need to be bulkier) break easy!
I also have two of the 'pickle fork' style that are hammered in to the joint part-line... one that is too wide for mini joints. I don't tend to use these much as they generally wreck the rubber seal boots.
My method with the lever press type is to undo the nut a few turns, fit the ball joint press and position it as good as possible before tightening it up until I get a bit nervous, then another couple of turns. If it hasn't let go, then I usually go do something else for a while, edging it up another quarter or half turn as I wander past from time to time. At some stage it will give up

Sometimes I leave it overnight and find it done by morning. They are not all that stubborn though
