Personally I have never really seen compassion as something to cultivate anyway. It generally refers to sharing the pain of other people, or of your own somehow. Pain is all too common and there is no need to practice experiencing pain. Even so, it can't really be avoided that compassion will increase once anger and fear decrease. There are a lot of things that get in the way of properly seeing yourself or everyone else. I get that compassion is promoted as a good thing because it gets around those kinds of barriers that keep people living in their own isolated existences - I just think it works the other way around. The barriers fall first, to some extent, and when they have sufficiently softened compassion can make a showy deal of pushing down more of them. So if you want to practice and cultivate something, I would suggest learning to enjoy seeing any sign of pleasure and satisfaction. Do this to the point where you can be happy when something good happens even if you had been in a bad mood. Let it generalize to the point where you can enjoy happiness whether it is your own or someone else's. The point is to soften your own obstacles to reaching outward. It doesn't matter if you find it easier to start on the outside and work inward, or start on the inside and work outward. Positive emotions are going to make the barriers grow thinner and negative emotions tend to build up new layers. That's why I don't think it is a good thing to practice experiencing more of anyone's pain. Let it come when it does, without fighting it - because resisting pain magnifies it. That's true of physical and emotional pain. It is instinctive and automatic to resist pain. Training in compassion is probably meant to make this resistance less automatic. You may also find that resistance toward enjoying the pleasure of people you dislike or even yourself. This resistance will also be automatic. I just think that it is better to spend more time working on allowing more enjoyment into your life instead of allowing in more pain.