Recent works on data-driven sketch-based modeling use either voxel grids or normal/depth maps as geometric representations compatible with convolutional neural networks. While voxel grids can represent complete objects-including parts not visible in the sketches-their memory consumption restricts them to low-resolution predictions. In contrast, a single normal or depth map can capture fine details, but multiple maps from different viewpoints need to be predicted and fused to produce a closed surface. We propose to combine these two representations to address their respective shortcomings in the context of a multi-view sketch-based modeling system. Our method predicts a voxel grid common to all the input sketches, along with one normal map per sketch. We then use the voxel grid as a support for normal map fusion by optimizing its extracted surface such that it is consistent with the re-projected normals, while being as piecewise-smooth as possible overall. We compare our method with a recent voxel prediction system, demonstrating improved recovery of sharp features over a variety of man-made objects.