We develop methods for listing, for a given 2-group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order 128 and two of order 1024. Our long term goal is to make a wider, more systematic search for exotic fusion systems over 2-groups of small order.