Structure from motion algorithms typically do not use external geometric constraints, e.g., the coplanarity of certain points or known orientations associated with such planes, until a final post-processing stage. In this paper, it is shown how such geometric constraints can be incorporated early on in the reconstruction process, thereby improving the quality of the estimates. The approaches studied include hallucinating extra point matches in planar regions, computing fundamental matrices directly from homographies, and applying coplanarity and other geometric constraints as part of the final bundle adjustment state. Experimental results indicate that the quality of the reconstruction can be significantly improved by the judicious use of geometric constraints.