Milankovitch proposed that Earth resides in an interglacial state when its spin axis both tilts to a high obliquity and precesses to align the Northern Hemisphere summer with Earth's nearest approach to the Sun. This general concept has been elaborated into hypotheses that precession, obliquity or combinations of both could pace deglaciations during the late Pleistocene. Earlier tests have shown that obliquity paces the late Pleistocene glacial cycles but have been inconclusive with regard to precession, whose shorter period of about 20,000 years makes phasing more sensitive to timing errors. No quantitative test has provided firm evidence for a dual effect. Here I show that both obliquity and precession pace late Pleistocene glacial cycles. Deficiencies in time control that have long stymied efforts to establish orbital effects on deglaciation are overcome using a new statistical test that focuses on maxima in orbital forcing. The results are fully consistent with Milankovitch's proposal but also admit the possibility that long Southern Hemisphere summers contribute to deglaciation.