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Calculations of spin-injected vertical-cavity surface-emitting lasers (VCSELs) are presented using an efficient algorithm for solution of the steady-state rate equations in the spin-flip model. The effects of spin relaxation, birefringence, electron and photon lifetimes, linewidth factor, and the magnitude and ellipticity of the pumping are investigated. After a review of published values for spin relaxation rates in semiconductors of interest for VCSELs, the dependence of spin relaxation times in GaInNAs quantum wells on N content and well width is calculated for the Elliot-Yafet process. The results, which show good agreement with experiment, are used in simulations of spin-injected GaInNAs VCSELs to determine the dependence of polarization control on well width.