Aspect-oriented programming is a promising paradigm that challenges traditional notions of program modularity. Despite its increasing acceptance, aspects have been documented to suffer limited reuse, hard to predict behavior, and difficult modular reasoning. We develop an algebraic model that relates aspects to program transformations and uncovers aspect composition as a significant source of the problems mentioned. We propose an alternative model of composition that eliminates these problems, preserves the power of aspects, and lays an algebraic foundation on which to build and understand AOP tools. 1