It seems like compromise is never the first thing we think of when we are in an argument. When people realize they have disagreements it is tempting to amplify or hyperfocus on those differences. So many of my clients come to work on issues that constitute a small fraction of the relationship in question. Couples will spend an hour talking about disagreements without acknowledging all of the issues that they agree on. Sometimes, it is good to remember what is going well.
Compromise happens when couples build bridges and think outside of the box for possible solutions. Very few problems have only one or even two solutions. One of the best skills to help you reach a compromise is to listen to what your partner is saying and start talking about the issues you agree with. This can help you both be on the same side of the table and not engaged in a chess match. It may be possible for both people to get what they want. However, with any compromise, you may not get everything you are asking for. Sometimes it is a good idea to ask yourself "is this the hill I want to die on" and be able to move on if it isn't. Remember, you are working with your partner to solve problems. Your partner is not the problem you are solving.