A unified minimum-residue approach is presented to the use of classical conservation laws for determination of the orientation and motion of a plasma discontinuity, using data from a single spacecraft that traverses the discontinuity and makes measurements, not only on its two sides but also within it. The method is a generalization of the minimum Faraday residue (MFR) analysis technique described by Khrabrov and Sonnerup (1998a). It includes not only the standard MHD conservation laws for mass, momentum, total energy, and (where applicable) entropy, but also magnetic flux conservation from Faraday's law, absence of magnetic poles from $nabla$ ¿ B = 0, and electric charge conservation from Amp¿re's law. A method, denoted by COM, for combining the results from more than one conservation law into a single optimal determination of the orientation and motion is presented, along with a general approach to the application of a certain class of constraints that can be placed on the vector normal to the discontinuity. The methodology, which is applicable to many types of discontinuity, including shocks, is illustrated by analysis of one magnetopause encounter by two of the four Cluster spacecraft (C1 and C3). The results from the various individual methods have considerable spread. However, in favorable circumstances and by exercising considerable care, the vector normal to the magnetopause from COM can be accurate to within a couple of degrees. For the C1 crossing, believed to be nearly a tangential discontinuity, albeit with signatures of incipient reconnection, the magnetopause speed (-56 km s-1) from COM appears accurate to within a few km s-1. The plasma flow across the magnetopause and the normal field component are both very nearly zero, and the results are consistent with those obtained from timing of the layer as it crosses the four Cluster spacecraft (assuming a constant thickness of the layer). The results for the velocity of the magnetopause and for the plasma flow across the layer are less consistent for the C3 crossing, believed to be a rotational discontinuity. For this crossing the presence of a component of the magnetic field along the normal direction could not be established with certitude. It is likely that the lower quality of the results for this crossing is caused by local multidimensional structure of the magnetopause.