The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form, For the spacecraft problem, they are both constructed using the method of integrator backstepping. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law.