  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
$\Delta\mstop = 0.42$ 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
