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We study the elliptically polarized states in the spin-flip model for vertical-cavity-surface-emitting lasers. The stability analysis reveals some unexpected features. In correspondence with particular values of the birefringence parameter, which are shown to scale very simply with the ratio of the spin-flip rate to the linewidth enhancement factor, the stability domain can be quite large. Moreover, in some cases two different dynamical regimes can arise from the destabilization of the elliptically polarized states, and they can coexist in a finite interval of the pump parameter. Finally, we show that the bifurcation from the lower frequency linearly polarized state to the elliptically polarized states can be subcritical when the linewidth enhancement factor is roughly smaller than 1