Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l(min). This convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavorable for a stem to be shorter than l(min) and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behavior of the Sadler-Gilmer model when an energetic contribution from chain folds is included.