Maintenance on the Conceptual Schema of a database is necessary when the current data structure can’t meet changed functional requirements. An additional requirement, not expressed in the demand for change, is to minimize the impact of change. The problem of minimizing impact of change on the data is often postponed to the implementation phase when data have to be migrated into the new structure. We propose a method to address the problem of Conceptual Schema evolution in an earlier phase, and introduce the notion of Majorant Schema to support the application of the method. The advantage of the approach is that a more graceful schema evolution is ensured because a broader range of design alternatives is investigated. Other benefits are the early attention for the impact of change, and a better preparation of the data migration effort. Experiences show that the method is primarily suited to minor changes.