Aspect oriented programming aims at achieving better modularization for a system's crosscutting concerns in order to improve its key quality attributes, such as evolvability and reusability. Consequently, the adoption of aspect-oriented techniques in existing (legacy) software systems is of interest to remediate software aging. The refactoring of existing systems to employ aspect-orientation will be considerably eased by a systematic approach that will ensure a safe and consistent migration. In this paper, we propose a refactoring and testing strategy that supports such an approach and consider issues of behavior conservation and (incremental) integration of the aspect-oriented solution with the original system. The strategy is applied to the JHotDraw open source project and illustrated on a group of selected concerns. Finally, we abstract from the case study and present a number of generic refactorings which contribute to an incremental aspect-oriented refactoring process and associate particular types of crosscutting concerns to the model and features of the employed aspect language. The contributions of this paper are both in the area of supporting migration towards aspect-oriented solutions and supporting the development of aspect languages that are better suited for such migrations.