Scaling analysis shows that the mean thickness of an ice sheet depends on the product of two poorly known quantities, the ice viscosity and the net snow accumulation rate. We adjust the viscosity of an ice sheet in order to get a consistent value of this product for the present-day ice sheet volume and area given the net snow accumulation rate calculated by an atmospheric general circulation model (GCM). We then hold this artificial rheology constant in further numerical experiments. We hope that in doing so we can partially compensate for systematic GCM errors in simulating the snow accumulation rate, and, therefore, thickening/thinning of ice sheets will depend mostly on the tendency in the net accumulation change rather than on its absolute value. Using this approach, the response of the Greenland and Antarctic ice sheets to doubling CO2 concentration is simulated and the horizontal distribution of possible thickening/thinning of polar ice obtained. We find that, initially, the region of thickening ice is close to the area of increased snowfall rate, but later it significantly changes under the influence of internal ice flow dynamics. The sea-level changes predicted by our experiments agree with some empirical estimates. The sensitivity experiment with assigned basal sliding does not show significant changes in the large-scale ice topography, meaning, for example, that there is no indication of a possible disintegration of the West Antarctic ice sheet. At the same time, the regional thickening/thinning of ice (and consequently the sea-level change) depends strongly on processes at the ice sheet bottom.