In this work, we consider the dense reconstruction of specular objects. We propose the use of a specularity constraint, based on surface normal/depth consistency, to define a matching cost function that can drive standard stereo reconstruction methods. We discuss the types of ambiguity that can arise, and suggest an aggregation method based on anisotropic diffusion that is particularly suitable for this matching cost function. We also present a controlled illumination setup that includes a pair of cameras and one LCD monitor, which is used as a calibrated, variable-position light source. We use this setup to evaluate the proposed method on real data, and demonstrate its capacity to recover high-quality depth and orientation from specular objects.