Most supersymmetric models predict new particles within the reach of the next generation of colliders. For an understanding of the model structure and the mechanism(s) of electroweak symmetry breaking, it is important to know the masses of the new particles precisely. The measurement of the mass of the scalar partner of the top quark (stop) at an e+e- collider is studied. A relatively light stop is motivated by attempts to explain electroweak baryogenesis and can play an important role in dark matter annihilation. A method is presented which makes use of cross-section measurements near the pair-production threshold as well as at higher center-of-mass energies. It is shown that this method does not only increase the statistical precision, but also reduces the influence of systematic uncertainties, which can be important. Numerical results are presented, based on a realistic event simulation, for two signal selection strategies: using conventional selection cuts, and using an Iterative Discriminant Analysis (IDA). While the analysis of stops is particularly challenging due to the possibility of stop hadronization and fragmentation, the general procedure could be applied to many precision mass measurements.