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A new algorithı is described for accurate computation of horizontal and vertical stereoscopic disparities of specular points, relative to nearby surface points. Knowledge of such disparities is shown to rcstrict principal curvatures (with known light-source position) to lie on a hyperbolic constraint-curve. Monocular appearance of specularities is known also to constrain surface shape. We show that, at best, there remains a forfold ambiguity of local sırface curvature. In the case of a light source that is of unknown shape but known to be compact (in a precise sense), elongated specularities have geometrical significance. The “axis” of such a specularity, back-projected onto the surface tangent plane, approximates to a line of curvature. The approximation improves as the specularity becomes more elongated and the source more compact.