A viscous, incompressible fluid is enclosed between two infinitely long coaxial cylinders. The entire system is assumed to be rotating initially as a rigid body with angular velocity Ω. At time t = 0, the outer cylinder is impulsively stopped. The resulting unsteady Couette flow is subject to centrifugal instabilities. Energy theory (strong stability) calculations have been performed for both axisymmetric and nonaxisymmetric disturbances to verify that the most dangerous mode is axisymmetric. The results include global stability bounds, lower bounds on the onset time, and Ior upper bounds on the decay times, and are compared to previous marginal stability results for the same basic state.