There is at present a controversy concerning the extent and thickness of the Innuitian Ice Sheet during the last glacial maximum (ca. 18 000 BP). Here, both a thick, extensive Innuitian Ice Sheet and a thin, limited ice sheet are isostatically modelled by employing disc-shaped elements and a radially symmetric Maxwellian Earth. The predicted relative sea-level curves for both models are compared with new data from Thores River, northernmost Ellesmere Island, and data from 29 other sites located in and around the Queen Elizabeth Islands. The data from Thores River are presented as an illustrative case study that particularly emphasizes the difficulty of relating sample elevations to ancient sea levels in this region. At all 30 sites, the relative sea-level data overwhelmingly favour the thick, extensive ice model. The hypothesis of tectonic uplift to explain the high raised beaches (> 100 m) found on Ellesmere Island and elsewhere in the region is rejected. The residual uplift of the thin, limited model is not spatially coherent, nor is it likely that tectonic uplift would exactly mimic the distinctive postglacial uplift. To reconcile geomorphological evidence (in the form of the preservation of preglacial maximum sediments and the general lack of glacial deposits) and the presence of high raised beaches, it is proposed that the Innuitian Ice Sheet was for part, possibly most, of its history a cold-based ice sheet (i.e., frozen to its bed).