For me, I've felt at least these types of compersion;
1) I have had sex with someone who really knew how to do it. We had fun times but there is someone I heavily suspect they would be even more compatible with. I love this person, I want them to experience the fullness of joy, also of sexual joy. I know that the person I've had sex with is interested in my other love. So to me, it seems natural to try to make sure that they at least consider the possibility of getting it on (without me).
2) I see someone treating their loved ones with respect and love. They want to share their loves with me, not because they are afraid that the relationship would end otherwise or because they want to get their own jollies out of it. They are just good at sharing, like someone who has enough to get by themselves might want to share from their good fortune to others less well-to-do. They understand the philosophy behind it. So compersion tinged with gratefulness and admiration.
3) I am with someone and thoroughly enjoying my self. For some reason, there is something I can't fully give to this other person - something they can do without, an interest perhaps that I don't share. I would encourage them to the best of my ability to seek out someone who shares that interest with them. A good example, like Mono pointed out, would be me dating a bisexual and wanting them to find a male partner as well.
So for me, compersion is a combination of wanting somebody to experience the fullness of joy available to them and also feeling that someone I am with is just too good NOT to share.
Me: bi female in my twenties