In order to respond to changing requirements and advances in technology, system and software architectures must evolve during their lifetimes. Usually, in this evolution, several key components of the architecture are replaced. Achieving successful architecture evolution at a reasonable cost and effort is difficult. It requires many architectural and technological decisions. This paper describes an approach, called 3RDBA, that facilitates replacing a key component in a long-living architecture. It is based on systematically gathering all information needed to make well-founded decisions regarding evolution of the architecture. The approach consists of an exploration, consolidation and migration cycle. Each cycle contains four steps: Requirements, Design, Build and Analyze. 3RDBA enables construction and evaluation of several alternative architecture realizations together with a migration path from the existing architecture towards the selected, new architecture. We describe how we have successfully applied this approach to support the evolution of a medical imaging system architecture.