Abstract. Over the last glacial cycle, ice sheets and the resultant glacial isostatic adjustment (GIA) rearranged river systems. As these riverine threads that tied the ice sheets to the sea were stretched, severed, and restructured, they also shrank and swelled with the pulse of meltwater inputs and time-varying drainage basin areas, and sometimes delivered enough meltwater to the oceans in the right places to influence global climate. Here I present a general method to compute past river flow paths, drainage basin geometries, and river discharges, by combining models of past ice sheets, glacial isostatic adjustment, and climate. The result is a time series of synthetic paleohydrographs and drainage basin maps from the Last Glacial Maximum to present for nine major drainage basins – the Mississippi, Rio Grande, Colorado, Columbia, Mackenzie, Hudson Bay, Saint Lawrence, Hudson, and Susquehanna/Chesapeake Bay. These are based on five published reconstructions of the North American ice sheets. I compare these maps with drainage reconstructions and discharge histories based on a review of observational evidence, including river deposits and terraces, isotopic records, mineral provenance markers, glacial moraine histories, and evidence of ice stream and tunnel valley flow directions. The sharp boundaries of the reconstructed past drainage basins complement the flexurally smoothed GIA signal that is more often used to validate ice-sheet reconstructions, and provide a complementary framework to reduce nonuniqueness in model reconstructions of the North American ice-sheet complex.