Due to two improvements in cavity design, low-threshold lasing is achieved in oxidized vertical-cavity surface-emitting lasers incorporating upper dielectric distributed Bragg reflectors. Intracavity absorption is reduced by removal of a heavily p-type contact layer and the use of a low-loss MgF-ZnSe upper mirror. We report sub-100 mu A lasing for a 7-mu m diameter device, and sub-40 mu A lasing for a 3-mu m diameter device. The low-loss cavity design also allows for highly multimode operation at a low-bias current of 600 mu A in a detuned cavity.