Measurements of quantum oscillations in the cuprate superconductors afford an opportunity to assess the extent to which their electronic properties yield to a description rooted in Fermi-liquid theory. However, such an analysis is hampered by the small number of oscillatory periods observed in the accessible magnetic field range. Here we employ a genetic algorithm to globally model the field, angular and temperature dependence of the quantum oscillations observed in the resistivity of YBa 2 Cu 3 O 6.59 . This approach successfully fits an entire data set to a Fermi surface consisting of two small, quasi-two-dimensional cylinders, rather than the large Fermi surface predicted by conventional electronic-structure calculations. A key result is the first identification of the effects of Zeeman splitting, indicating that the quasiparticles behave as nearly free spins, constraining the source of the Fermi-surface reconstruction to something other than a spin-density wave with moments perpendicular to the magnetic field. © 2011 Macmillan Publishers Limited. All rights reserved.