Polarization selection in small-area vertical-cavity surface-emitting lasers is studied experimentally in dependence of injection current and substrate temperature in the vicinity of the minimum threshold condition. Polarization switching from the low to the high frequency fundamental spatial mode is demonstrated. The effective birefringence displays a minimum in the transition region. The observation of dynamical transition states hints to the relevance of nonlinear effects. A comparison to the predictions of the San Miguel-Feng-Moloney model based on phase-amplitude coupling is given.