Paleo-ice sheet reconstructions are complicated by large uncertainties, particularly since it is usually only possible to infer thickness from indirect means such as the response of glacial isostatic adjustment (GIA). GIA itself has large uncertainties with respect to the rheological structure of the Earth, and it is possible to get multiple possible best fitting ice sheet configurations using different Earth models. Usually the best geological constraints for paleo-ice sheets are ice margin location, via dating methods and geomorphological features. Using the program ICESHEET (Gowan et al 2016), it is possible to exploit this knowledge and create glaciologically consistent ice sheet reconstructions for use in GIA modeling. We demonstrate this by applying them to the North American Laurentide and Innuitian ice sheets, and show that it is possible to have an ice sheet that has a much lower profile than other GIA constrained reconstructions such as ICE-6G, GLAC-1 and ANU. A lower profile ice sheet has profound implications for past climate reconstructions, including radically different atmospheric and Atlantic Ocean circulation at the Last Glacial Maximum. Such a reconstruction is better able to fit geological constraints in the near field, but are at odds with global sea level reconstructions that require much larger ice volume. We discuss possible solutions to this issue. Another benefit of ICESHEET is that it does not require climatic information, since the ice thickness is adjusted by changing a spatially and temporarily variable basal shear stress parameter. Using these reconstructions in climate models do not face the circularity of dynamic ice sheet models that require a climatic input that was often derived from a-priori ice sheet reconstructions.