Many people score high on two or three resolution styles. That's because people use different styles depending on the context. You can choose the style you use strategically and deliberately. For example:
- With your boss - you might use an accommodating style
- With your friends - you might be compromising
- With the cable company - you might use a competing style
Because each of the styles has an appropriate use, it's a good idea to understand and practice each one. Before entering into a conflict, consider what the appropriate style to employ is - and don't be afraid to change strategies if it's not working. It's also helpful to analyze your opponent's style: If she is using a collaborating style, you'll want to adopt the same. If she is accommodating, you'll have to decide whether she really doesn't care about the outcome (in which case take what you can get), or whether there is a deeper issue which is going to cause her to be dissatisfied with the resolution.
There is a lot of more information about conflict resolution styles on the web. MIT has a particularly good site.