We focus on a recently proposed regression framework termed lattice regression, as applied to the construction of multidimensional color management look-up tables from empirical measurements. The key idea of lattice regression is that the construction of a look-up table should take into account the interpolation function used in its final implementation. Lattice regression solves for the look-up table (LUT) that minimizes the error of interpolating the empirical measurements (training samples) and regularization is added to promote smoothness and enable extrapolation. The main contribution of this paper is the proposal and analysis of using the thin-plate regularizer for lattice regression to produce smooth and accurate color transformations. Experiments with a consumer inkjet and laser printer show that the proposed regularizer obtains similar accuracy to the previously-proposed (and more complicated) combination of Laplacian and globalbias regularizers, and that both can create significantly more accurate and smoother results than a state-of-the-art locally linear approach.