  We consider a system with general decoherence and a quadratic dynamical
decoupling sequence (QDD) for the coherence control of a qubit coupled to a
bath of spins. We investigate the influence of the geometry and of the initial
conditions of the bath on the performance of the sequence. The overall
performance is quantified by a distance norm $d$. It is expected that $d$
scales with $T$, the total duration of the sequence, as $T^{\min
\{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer
and of the inner sequence, respectively. We show both numerically and
analytically that the state of the bath can boost the performance of QDD under
certain conditions: The scaling of QDD for a given number of pulses can be
enhanced by a factor of 2 if the bath is prepared in a highly symmetric state
and if the system Hamiltonian is SU(2) invariant.
