  To protect a quantum system from decoherence due to interaction with its
environment, we investigate the existence of initial states of the environment
allowing for decoherence-free evolution of the system. For models in which a
two-state system interacts with a dynamical environment, we prove that such
states exist if and only if the interaction and self-evolution Hamiltonians
share an eigenstate. If decoherence by state preparation is not possible, we
show that initial states minimizing decoherence result from a delicate
compromise between the environment and interaction dynamics.
