Prior to ~1 million years ago (Ma), variations in global ice volume were dominated by changes in obliquity; however, the role of precession remains unresolved. Using a record of North Atlantic ice rafting spanning the past 1.7 million years, we find that the onset of ice rafting within a given glacial cycle (reflecting ice sheet expansion) consistently occurred during times of decreasing obliquity whereas mass ice wasting (ablation) events were consistently tied to minima in precession. Furthermore, our results suggest that the ubiquitous association between precession-driven mass wasting events and glacial termination is a distinct feature of the mid to late Pleistocene. Before then (increasing), obliquity alone was sufficient to end a glacial cycle, before losing its dominant grip on deglaciation with the southward extension of Northern Hemisphere ice sheets since ~1 Ma.