In the deep ice cores drilled at the GRIP, NGRIP and GISP2 sites in Greenland and at Byrd Station and the summit of Law Dome in Antarctica, the mean crystal size increases with depth in the shallow subsurface and reaches steady values at intermediate depth. This behaviour has been attributed to the competition between grain-boundary migration driven crystal growth and crystal polygonization, but the effects of changing crystal dislocation density and non-equiaxed crystal shape in this competition are uncertain. We study these effects with a simple model. It describes how the mean height and width of crystals evolve as they flatten under vertical compression, and as crystal growth and polygonization compete. The polygonization rate is assumed to be proportional to the mean dislocation density across crystals. Migration recrystallization, which can affect crystal growth via strain-induced grain boundary migration but whose impact on the mean crystal size is difficult to quantify for ice at present, is not accounted for. When applied to the five ice-core sites, the model simulates the observed crystal-size profiles well down to the bottom of their steady regions, although the match for Law Dome is less satisfactory. Polygonization rate factors retrieved for the sites range from 10–5 to 10–2 a–1. We conclude that since crystal size and dislocation density evolve in a strongly coupled manner, consistent modelling requires multiple differential equations to track both of these variables. Future ice-core analysis should also determine crystal size in all three principal directions.