  Aperiodic dynamical decoupling (DD) sequences of $\pi$ pulses are of great
interest to decoherence control and have been recently extended from
single-qubit to two-qubit systems. If the environmental noise power spectrum is
made available, then one may further optimize aperiodic DD sequences to reach
higher efficiency of decoherence suppression than known universal schemes. This
possibility is investigated in this work for the protection of two-qubit
states, using an exactly solvable pure dephasing model including both local and
nonlocal noise. The performance of optimized DD sequences in protecting
two-qubit states is compared with that achieved by nested Uhrig's DD
(nested-UDD) sequences, for several different types of noise spectrum. Except
for cases with noise spectrum decaying slowly in the high-frequency regime,
optimized DD sequences with tens of control pulses can perform orders of
magnitude better than that of nested-UDD. A two-qubit system with highly
unbalanced local noise is also examined to shed more light on a recent
experiment. Possible experiments that may be motivated by this work are
discussed.
