A sharp interface model is developed to allow rapid discovery of exactly compatible or averagely compatible laminate twin patterns in a cubic-orthorhombic shape memory alloy system. Given an imposed strain state, the method finds a corresponding exactly compatible twin structure if one exists; otherwise, the method produces an averagely compatible solution. Two cases are considered: The first case allows austenite and martensite phases to be arbitrarily mixed. The second is an essentially flat austenite-martensite phase boundary, with an exactly compatible martensite laminate on one side. The results show several well-known configurations and also many new structures. A full search reveals the routes in strain space along which the two-phase structure can continuously evolve. The influence of the middle eigenvalue of the martensite transformation strain on twin patterns is explored.