Wrinkling of thin films is an easy-to-implement and low-cost technique to fabricate stretch-tunable periodic micro and nanoscale structures. However, the tunability of such structures is often limited by the emergence of an undesirable period-doubled mode at high strains. Predictively tuning the onset strain for period doubling via existing techniques requires one to have extensive knowledge about the nonlinear pattern formation behavior. Herein, a geometric prepatterning-based technique is introduced that can be implemented even with limited system knowledge to predictively delay period doubling. The technique comprises prepatterning the film/base bilayer with a sinusoidal pattern that has the same period as the natural period of the system. This technique has been verified via physical and computational experiments on the polydimethylsiloxane (PDMS)/glass bilayer system. It is observed that the onset strain can be increased from the typical value of 20% for flat films to greater than 30% with a modest prepattern aspect ratio (2·amplitude/period) of 0.15. In addition, finite element simulations reveal that (i) the onset strain increases with increasing prepattern amplitude and (ii) the delaying effect can be captured entirely by the prepattern geometry. Therefore, one can implement this technique even with limited system knowledge, such as material properties or film thickness, by simply replicating pre-existing wrinkled patterns to generate prepatterned bilayers. Thus, geometric prepatterning is a practical scheme to increase the operating range of stretch-tunable wrinkle-based devices by at least 50%.