associated with entangled states as well as non-entangled states? This is a significant issue because the ultimate goal of decoherence suppression is to suppress the decoherence of a completely unknown state and hence to preserve the quantum coherence of any type at the same time. Fortunately, for single-qubit cases: (i) there are already good insights into the difference between decoherence suppression for a known state and decoherence suppression for an unknown state [@lorenza3; @lorenza4] (with un-optimized DD schemes); and (ii) a very recent study [@QDD] showed that suppressing the longitudinal decoherence and the transverse decoherence of a single qubit at the same time in a “near-optimal" fashion is possible, by arranging different control Hamiltonians in a nested loop structure. Inspired by these studies, we are now working on an extended scheme to achieve efficient decoherence suppression in two-qubit systems, such that two or even more types of coherence properties can be preserved. Thanks to our explicit construction of the UDD control sequence for non-entangled and entangled states, some interesting progress towards this more ambitious goal is being made. For example, we anticipate that it is possible to preserve two types of quantum coherence of a two-qubit state at the same 