Advances in new Information Technologies (IT) and changes in the business environment such as globalization and competitive pressure have prompted organizations to embark on reengineering projects involving significant investments in IT and business process redesign. However, the evidence of payoff from such investments can be classified as mixed as best, a problem we partly attribute to the absence of a strong theoretical foundation to assess and analyze reengineering projects. We seek to apply complementarity theory and a business value modeling approach to address some questions involving what, when, and how much to reengineer. Complementarity theory is based on the notion that the value of having more of one factor increases by having more of another complementary factor. Further, related developments in the optimization of "supermodular" functions provide a useful way to maximize net benefits by exploiting complementary relationships between variables of interest. Combining this theory with a multi-level business value model showing relationships between key performance measures and their drivers, we argue that organizational payoff is maximized when several factors relating to IT, decision authority, business processes and incentives are changed in a coordinated manner in the right directions by the right magnitude to move toward an ideal design configuration. Our analysis further shows that when a complementary reengineering variable is left unchanged either due to myopic vision or self-interest, the organization will not be able to obtain the full benefits of reengineering due to smaller optimal changes in the other variables. We also show that by increasing the cost of changing the levels of design variables, unfavorable preexisting conditions (e.g., too much heterogeneity in the computing environment) can lead to reengineering changes of smaller magnitude than in a setting with favorable conditions.