At the Last Glacial Maximum (LGM), about 21,000 years before present, land-based ice sheets held enough water to reduce global mean sea level by 130 metres(1). Yet after decades of study, major uncertainties remain as to the distribution of that ice(2). Here we test four reconstructions of North American deglacial ice-sheet history(3-6) by quantitatively connecting them to high-resolution oxygen isotope (delta O-18) records from the Gulf of Mexico(7-11) using a water mixing model(12). For each reconstruction, we route meltwater(3-6) and seasonal runoff(13-16) through the time-evolving Mississippi drainage basin, which co-evolves with ice geometry(3-6) and changing topography as ice loads deform the solid Earth and produce spatially variable sea level in a process known as glacial isostatic adjustment(17). The delta O-18 records show that the Mississippi-drained southern Laurentide ice sheet contributed only 5.4 +/- 2.1 metres to global sea level rise, of which 0.66 +/- 0.07 metres were released during the meltwater pulse 1A event 14,650-14,310 years before present(18), far less water than previously thought(5,12,19). In contrast, the three reconstructions based on glacial isostatic adjustment(3-5) overpredict the delta O-18-based post-LGM meltwater volume by a factor of 1.6 to 3.6. The fourth reconstruction(6), which is based on ice physics, has a low enough Mississippi-routed meltwater discharge to be consistent with delta O-18 constraints, but also contains the largest LGM North American ice volume. This suggests that modelling based on ice physics may be the best way of matching isotopic records while also sequestering enough water in the North American ice sheets to match the observed LGM sea level fall(1).