Two two-level particles in a cavity, coupled to the cavity modes (thin lines) and subject to local control fields (thick lines). ((a), (b)) Frequency domain overlap of coupling spectrum (dotted) and modulation matrix elements (solid), resulting in modified decoherence matrix elements (shaded), for (a) Global modulation (ICP symmetry) and (b) Cross-decoherence elimination (IIP symmetry). (c) General modulation scheme.