Iceland provides a unique case study for glacial-isostatic adjustment (GIA) research. This is due to an underlying viscosity stratification (thin elastic lithosphere overlying a low-viscosity zone or LVZ) that differs greatly from what is usually considered for the continental regions that have experienced changes in glacial loading (thick elastic lithosphere and often no asthenosphere). An assessment of the importance of the LVZ thickness is examined within the context of sea-level change following the Last Glacial Maximum (LGM). Overall, based on estimates of the extent of the Iceland Ice Sheet derived from geomorphological evidence, and assuming a viscosity structure that is generally accepted by workers in this field, the present-day ongoing-isostatic adjustment resulting from the deglaciation following the LGM would be minimal. An alternate viscosity structure, involving a low-viscosity channel within a thicker lithosphere, as suggested by seismic studies, is also discussed. We find that provided the channel is sufficiently thick, then a response similar to that from a thin lithosphere may be obtained. The present-day situation around the Vatnajoekull Ice Cap is also examined, with predictions of crustal displacement compared with recent GPS measurements of vertical uplift. It is found that care must be shown when using GPS time series, as the expected viscosity structure under Vatnajoekull is such that inter annual mass-balance changes cause significant variability (mm scale) to local uplift rates.