I agree with Erin, compromise is rarely a good solution.
It tends towards lose/lose, and is used as "I'll give up what I want if you give up what you want and then we'll both feel like we've done the 'good' thing." This isn't the definition but it's often how it plays out in a relationship. Compromise normally comes from when two people in a relationship are defending their position on an issue, they've taken the issue on as themselves and now need to defend it. If you never took on the position, then you would have no need to defend it, but often the other person is still heavily defending theirs.
As I'm not yet in a relationship, so this is theory, but I have thought a lot about it. If you stand by your values and let them be your position, but without getting attached then you will see a solution that is win/win. If you present the solution often the other person will leap for it, as they can have what they want and still have their position. It is possible to have your cake and eat it too in human relationships. In Erin's example, the win/win situation for the videos was, strangely enough, watching exactly they wanted, and giving up the position that they had to watch them together and compromise.
Sometimes this looks odd too, like if you value Joy you might give up something not important to you, like TV, so that you can spend time with your wife creating Joy.
It's not always about being concrete either.
Lastly, if someone you are in a relationship keeps trying to dominate you and get you to do what they want and against your values, then you'll want to get that sorted. Sometimes people's values clash, and the relationship won't work as you are going in different directions. Those sorts of relationships are best ending on good terms, keeping in touch and perhaps when values change getting back together. There are other times when people haven't created their values, or aren't following them, so they come from having to be right all the time, or boss people around, or a pattern of behaviour they learnt. In that case, standing by your values and explaining why that sort of behaviour doesn't work is often the best course of action, but can destroy a relationship, if the other person still wants to keep on the same. It is best then again to break the relationship on good terms.
If at anytime you have to dishonour who you really are to fit in with how another person wants you to be, then there is a problem. Be fully true to yourself and you won't have to worry about conforming.