Rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only. However, this impossibility does no longer hold when the feedback is also a function of time, and explicit smooth time-varying feedbacks which locally asymptotically stabilize the attitude of a rigid spacecraft have previously been proposed by the authors and colleagues \cite{MO.SA}. Due to the smoothness of the control law, the stabilization is not exponential and the asymptotical convergence rate to the desired equilibrium is only polynomial in the worst cas e. Nevertheless, exponential convergence can be obtained by considering time-varyi ng feedbacks which are only continuous at the equilibrium. The present article proposes expl icit feedback control laws of this type.