In this paper we propose an approach to mitigate shadowing errors in LIDAR scan matching, by introducing a preprocessing step based on spherical gridding. Because the grid aligns with the LIDAR beam, it is relatively easy to eliminate shadow edges which cause systematic errors in LIDAR scan matching. As we show through testing on real and synthetic data from a mechanically spinning multi-channel LIDAR unit, our proposed algorithm provides better results than ground plane removal, the most common existing strategy for shadow mitigation. Unlike ground plane removal, our method applies to arbitrary terrains (e.g. shadows on urban walls, shadows in hilly terrain) while retaining key LIDAR points on the ground that are critical for estimating changes in height, pitch, and roll. In our experiments, we demonstrate how our technique drastically reduces error in NDT scan registration (compared to a standard Cartesian voxel grid) on real LIDAR point cloud data, and then conduct Monte-Carlo trials in a simulated environment to demonstrate how our proposed technique eliminates the systemic bias introduced by range-shadowing.