Many 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 symmetry breaking, it is important to know the masses of the new particles precisely. In this article 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 relic density. 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 not only increases the statistical precision, but also greatly reduces the 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). Our studies indicate that a precision of Δmtilde t1 = 0.42 GeV can be achieved, representing a major improvement over previous studies. While the analysis of stops is particularly challenging due to the possibility of stop hadronization, the general procedure could be applied to the mass measurement of other particles as well. We also comment on the potential of the IDA to discover a stop quark in this scenario, and we revisit the accuracy of the theoretical predictions for the neutralino relic density.