In this work we present the results of a new analytical model that examines the coupling between glacial erosion and orogen development. Surface processes are assumed to be glacially dominated, and tectonic activity is controlled by critical wedge mechanics. In these circumstances, we find that orogen width is strongly dependent on both the rate of accretion and on the rate of precipitation. The orogen size is linked to tectonic and climate changes via proportionality constants: the orogen width scales with the rate of accretion to between the 2/3rd and 2nd powers, and with the rate of precipitation to the 1/3rd and 5/4th powers. The value of the proportionality constants varies with the taper angle and the relative rates of ice deformation and sliding. In all cases, the sensitivities are higher than those calculated for fluvially-eroding critical wedge orogens. Analytical solutions are supported by the results of a numerical flow-line model. The flow-line model further predicts that uplift rates will be highest at, and just below, the equilibrium line altitude. If glacial ablation is largely a calving process, rock uplift in the wedge will be strongly focused towards the toe. The predicted response time of glaciated orogens to changes in climate and tectonic forcing is dependent upon the constants of erosion, the rheology, and the rate of precipitation. These analyses predict that actual orogens have variable e-folding response times, for example approximately 1.5 Myr for the Southern Alps of New Zealand and the Olympic Mountains of Washington State, and approximately 5.5 Myr for the European Alps.