Architectural design is a vital phase in the development of e-business applications. A suitable compromise must be determined taking into account business requirements, quality criteria and existing constraints (e.g. presence of legacy systems). This paper adopts the view that for a particular problem context, the architectural design process can be considered as a series of choices regarding the application of a number of architectural design strategies. The problem context described in the paper is common to a category of e-business applications that arise from the e-finance domain. Given a formal representation of this context, we identify and formalise a number of applicable design strategies and show the resulting architectures. We also represent the overall design process as a decision tree and show how quality models can be used to select the most appropriate architecture. The recommendations made by the models are checked against real data from existing projects.