Although the mechanism by which a kinesin-1 molecule moves individually along a microtubule is quite well-understood, the way that many kinesin-1 motor proteins bound to the same cargo move together along a microtubule is not. We identified a 60-amino-acid-long domain, termed Hinge 1, in kinesin-1 from Drosophila melanogaster that is located between the coiled coils of the neck and stalk domains. Its deletion reduces microtubule gliding speed in multiple-motor assays but not single-motor assays. Hinge 1 thus facilitates the cooperation of motors by preventing them from impeding each other. We addressed the structural basis for this phenomenon. Video-microscopy of single microtubule-bound full-length motors reveals the sporadic occurrence of high-compliance states alternating with longer-lived, low-compliance states. The deletion of Hinge 1 abolishes transitions to the high-compliance state. Based on Fourier transform infrared, circular dichroism, and fluorescence spectroscopy of Hinge 1 peptides, we propose that low-compliance states correspond to an unexpected structured organization of the central Hinge 1 region, whereas high-compliance states correspond to the loss of that structure. We hypothesize that strain accumulated during multiple-kinesin motility populates the high-compliance state by unfolding helical secondary structure in the central Hinge 1 domain flanked by unordered regions, thereby preventing the motors from interfering with each other in multiple-motor situations.