A knowledge-level analysis of complex tasks like diagnosis and design can give us a better understanding of these tasks in terms of the goals they aim to achieve and the different ways to achieve these goals. In this paper we present a knowledge-level analysis of redesign. Redesign is viewed as a family of methods based on some common principles, and a number of dimensions along which redesign problem solving methods can vary are distinguished. By examining the problem-solving behavior of a number of existing redesign systems and approaches, we came up with a collection of problem-solving methods for redesign and developed a task-method structure for redesign.In constructing a system for redesign a large number of knowledge-related choices and decisions are made. In order to describe all relevant choices in redesign problem solving, we have to extend the current notion of possible relations between tasks and methods in a PSM architecture. The realization of a task by a problem-solving method, and the decomposition of a problem-solving method into sub-tasks are the most common relations in a PSM architecture. However, we suggest to extend these relations with the notions of task refinement and method refinement. These notions represent intermediate decisions in a task-method structure, in which the competence of a task or method is refined without immediately paying attention to its operationalization in terms of subtasks. Explicit representation of this kind of intermediate decisions helps to make and represent decisions in a more piecemeal fashion.