The horizontal-gradient method has been used since 1982 to locate density or magnetic boundaries from gravity data (Cordell, 1979) or pseudogravity data (Cordell and Grauch, 1985). The method is based on the principle that a near-vertical, fault-like boundary produces a gravity anomaly whose horizontal gradient is largest directly over the top edge of the boundary. Magnetic data can be transformed to pseudogravity data using Fourier techniques (e.g., Hildenbrand, 1983) so that they behave like gravity data; thus the horizontal gradient of pseudogravity also has maximum magnitude directly over the boundary. The method normally is applied to gridded data rather than to profiles. The horizontal-gradient magnitude is contoured and lines are drawn or calculated (Blakely and Simpson, 1986) along the contour ridges. These lines presumably mark the top edges of magnetic or density boundaries. However, horizontal-gradient magnitude maxima (gradient maxima) can be offset from a position directly over the boundary for several reasons. Offsets occur when boundaries are not near-vertical, or when several boundaries are close together. This note predicts these offsets. Many other factors also cause offsets, but they are less straightforward and usually are only significant in local studies; we discuss these factors only briefly.