Consider a free and minimal topological dynamical system and the corresponding crossed-product C*-algebra. We show that, under an assumption of Rokhlin property and an assumption of Cuntz comparison of open sets, the radius of comparison of the C*-algebra is at most the half of the mean (topological) dimension of the dynamical system. Moreover, still under these two assumptions, if the mean dimension is zero, then the C*-algebra is Jiang-Su stable or finite dimensional. This includes all free and minimal actions by Z^d and some other systems.