We show that using a nonconvex penalty term to regularize image reconstruction can substantially improve the preservation of object shapes. The commonly-used total-variation regularization, ∫|∇u|, penalizes the length of object edges. We show that ∫|∇u|^p, 0 < p < 1, only penalizes edges of dimension at least 2 - p, and thus finite-length edges not at all. We give numerical examples showing the resulting improvement in shape preservation.