We present the results of a new numerical model of the late glacial western Laurentide Ice Sheet, constrained by observations of glacial isostatic adjustment (GIA), including relative sea level indicators, uplift rates from permanent GPS stations, contemporary differential lake level change, and postglacial tilt of glacial lake level indicators. The later two datasets have been underutilized in previous GIA based ice sheet reconstructions. The ice sheet model, called NAICE, is constructed using simple ice physics on the basis of changing margin location and basal shear stress conditions in order to produce ice volumes required to match GIA. The model matches the majority of the observations, while maintaining a relatively realistic ice sheet geometry. Our model has a peak volume at 18,000 yr BP, with a dome located just east of Great Slave Lake with peak thickness of 4000 m, and surface elevation of 3500 m. The modelled ice volume loss between 16,000 and 14,000 yr BP amounts to about 7.5 m of sea level equivalent, which is consistent with the hypothesis that a large portion of Meltwater Pulse 1A was sourced from this part of the ice sheet. The southern part of the ice sheet was thin and had a low elevation profile. This model provides an accurate representation of ice thickness and paleo-topography, and can be used to assess present day uplift and infer past climate. (C) 2016 Elsevier Ltd. All rights reserved.