Perturbation of divide position is considered by a linearization about the Vialov-Nye solution and also about related solutions with 0(1) relief. Relaxation times of one-sixteenth the fundamental thickness/accumulation-rate time-scale are found for the Vialov-Nye configuration, while substantial basal topography can halve the rate of relaxation. Steady divide position is most sensitive to anti-symmetric accumulation-rate distributions near the divide, but transient divide motion is most strongly excited by anti-symmetric accumulation rate variations halfway between the margin and the divide. Relaxation times for the Antarctic Peninsula divide position are estimated to be around 200 years, while the larger Greenland ice sheet has a divide-position relaxation time of around 600 years. Modelling accumulation rate as a white-noise process permits analysis of divide perturbation as a (stochastic) Ornstein-Uhlenbeck process, where the standard deviation of the response is proportional to the standard deviation of the forcing. If observed accumulation-rate variability in the Antarctic Peninsula were antisymmetric about the divide, it would be sufficient to force the divide position to fluctuate with standard deviation 10-20 times the depth of the ice sheet. There appears to be sufficient noise to cause Raymond bumps to be spread significantly. More data on the statistical variation of accumulation with position are needed. Random forcing will increase the complexity of any fold structures created in the divide region and in particular the number of such structures intersecting any borehole.