Despite the money and sweat that go into new instructional technologies, they do not produce the overall high level of student performances that societies seek. More effective teaching calls for a profound solution. It requires a coordinate triad of factors: a proper science, the correct organizational structure, and an engineering instructional technology. This second of a series of articles on the Triad Model of Education concentrates on instructional engineering. The instructional engineering drawn from the science is contingency-based. Contingency-based instructional systems always handle the inevitable two components of instruction: the repertoires of students and the setups that shape those repertoires. The setup component features five elements: subject matter, objectives, quality control, presentation modes, and logistics. The repertoire component consists of the governance of repertoires—event and lingual governed, the type of repertoire—knowing, solving, and creating, and the variability of the repertoire—convergent and divergent. These elements, and their required engineering, reveal an instructional task more complex than previously considered. Progress with such complexity occurs only when all components of the triad are in place.