Despite repeated announcements of its death or uselessness, the 'linear model' of science-technology relations persists, the notion that fundamental scientific research precedes applied studies that in time generate technological advances. This article undertakes first to revisit investigations and critiques of the model, and to remind historians of technology that intriguing alternatives to it have been developed. Second, using the case study of Cold War military jet propulsion, it argues that innovative, complex technologies have been created without reliable understanding of scientific fundamentals. These were messy, non-linear, and failure-filled processes, to be sure, yet they may well prove to have been more the rule than the exception, once scholars pursue richly textured studies of technical practice in experimental development. Ultimately, project needs to overcome engineering obstacles in technological innovation may provide the platforms and the funding to support basic scientific research as well, reversing the linear model's expected flows.