Computed Tomography is increasingly employed for nondestructive evaluation, with the aim of reconstructing a surface mesh of a scanned object from radiographic projections. State-of-the-art algorithms first reconstruct a voxel grid and then extract a surface mesh using existing meshing algorithms, often leading to stair-like aliasing artifacts along the grid axes, due to the grid's orientation-dependent resolution. We circumvent such artifacts in filtered backprojection reconstructions by optimizing the mesh's vertex positions using information taken directly from the projections, rather than from a voxel grid. We show that our approach reduces stair artifacts both visibly and measurably, at relatively little additional computational cost. Our method can be tied into existing mesh extraction algorithms and removes stair artifacts almost entirely.