  The optimal $N$-pulse dynamical decoupling discovered by Uhrig for a
spin-boson mmodel [Phys. Rev. Lett, {\bf 98}, 100504 (2007)] is proved to be
universal in suppressing to $O(T^{N+1})$ the pure dephasing or the longitudinal
relaxation of a qubit (or spin-1/2) coupled to a generic bath in a short-time
evolution of duration $T$. It is also found that for the purpose of suppressing
the longitudinal relaxation, an ideal Uhrig $\pi$-pulse sequence can be
generalized to a sequence consisting of the ideal one superimposed with
finite-duration pulses satisfying certain symmetry requirements.
