  Dynamical decoupling can be used to preserve arbitrary quantum states despite
undesired interactions with the environment, using control Hamiltonians
affecting the system only. We present a system-independent analysis of
dynamical decoupling based on leading order decoupling error estimates, valid
for bounded-strength environments. Using as a key tool a renormalization
transformation of the effective system-bath coupling Hamiltonian, we delineate
the reliability domain of dynamical decoupling used for quantum state
preservation, in a general setting for a single qubit. We specifically analyze
and compare two deterministic dynamical decoupling schemes -- periodic and
concatenated -- and distinguish between two limiting cases of fast versus slow
environments. We prove that concatenated decoupling outperforms periodic
decoupling over a wide range of parameters. These results are obtained for both
``ideal'' (zero-width) and realistic (finite-width) pulses This work extends
and generalizes our earlier work, Phys. Rev. Lett. 95, 180501 (2005).
