The secular instability of Maclaurin spheroids due to the combined effects of viscosity and gravitational-radiation reaction is investigated, and it is found that the instabilities caused by each of these dissipative effects tend to cancel each other. All 'second harmonic mode' perturbations of Maclaurin spheroids are examined in order to determine precisely how the cancellation of instabilities occurs. The results show that only the toroidal modes have instabilities induced by the dissipative forces, that the particular point at which the secular instability actually sets in depends on the ratio (X) of the strengths of the viscous and gravitational-reaction forces, and that instability cancellation occurs because viscous dissipation and radiation reaction cause different modes to become unstable. In particular, the mode which is not unstable to one dissipative force is found to be stabilized by that force. It is concluded that for a specific choice of X, the stable portion of the Maclaurin sequence can be extended all the way to the point of onset of dynamical instability.