The factors driving glacial changes in ocean overturning circulation are not well understood. On the basis of a comparison of 20 climate variables over the past four glacial cycles, the SPECMAP project proposed that summer insolation at high northern latitudes (that is, Milankovitch forcing) drives the same sequence of ocean circulation and other climate responses over 100-kyr eccentricity cycles, 41-kyr obliquity cycles and 23-kyr precession cycles. SPECMAP analysed the circulation response at only a few sites in the Atlantic Ocean, however, and the phase of circulation response has been shown to vary by site and orbital band. Here we test the SPECMAP hypothesis by measuring the phase of orbital responses in benthic delta(13)C (a proxy indicator of ocean nutrient content) at 24 sites throughout the Atlantic over the past 425 kyr. On the basis of delta(13)C responses at 3,000-4,010 m water depth, we find that maxima in Milankovitch forcing are associated with greater mid-depth overturning in the obliquity band but less overturning in the precession band. This suggests that Atlantic overturning is strongly sensitive to factors beyond ice volume and summer insolation at high northern latitudes. A better understanding of these processes could lead to improvements in model estimates of overturning rates, which range from a 40 per cent increase to a 40 per cent decrease at the Last Glacial Maximum and a 10-50 per cent decrease over the next 140 yr in response to projected increases in atmospheric CO(2) (ref. 4).