A simple analytical solution is presented to the problem of determining the orientation and motion of a one-dimensional discontinuity in plasma velocity and density, measured by a single spacecraft as the discontinuity moves past it. The method developed is called Minimum Massflux Residue (MMR). Illustrations of the method, based on Cluster measurements in the dawnside magnetopause region, are given, and the results are compared with those obtained by other methods, such as Minimum Faraday Residue (MFR) analysis and minimum variance analysis of the magnetic field combined with deHoffmann-Teller frame determination (MVAB/HT). The results indicate that the Cluster plasma measurements are of sufficiently high quality for MMR to yield normal vectors and magnetopause speeds that agree well with those obtained from MFR and also from a constrained version of MVAB/HT (the constraint being $langle$B$rangle$ ¿ n = 0). We also show how results from more than one method can be combined to produce a single prediction of the normal vector and speed.