Nonlinear equilibrium states characterized by strongly localized vortex pairs are calculated in the linearly stable parameter region of counterrotating Taylor-Couette flow. These subcritical states are rotating waves whose region of existence is consistent with the critical threshold for relaminarization observed in experiments. For sufficiently rapid outer cylinder rotation the solutions extend beyond the static inner cylinder case to corotation, thus exceeding, for the first time, the boundary defined by the inviscid Rayleigh's stability criterion.