Z-source energy conversion is a recent concept introduced for adding voltage-boost functionality to the otherwise buck-only dc-ac inverter. The same concept can equally be extended to other converter topologies including the indirect ac-ac matrix converter, where only a single Z-source impedance network needs to be inserted to its intermediate dc-link. Because of such a simple insertion, topological extension of the indirect Z-source matrix converter is viewed as trivial with its operating states easily deducible from its existing dc-ac counterpart. In contrast, modulation of the extended indirect ac-ac entity is judged as nontrivial and not at all obvious if advantages like buck-boost flexibility, minimum commutation count and ease of implementation are to be attained simultaneously, in addition to sinusoidal input and output quantities commonly set as objectives for ac-ac energy conversion. Attaining these advantages simultaneously is no doubt important since any shortfalls or compromises would make it even harder to justify for those passive components introduced to the otherwise “all semiconductor” indirect matrix converter. Bringing forth these advantages by unveiling related optimal modulation theories is therefore a relevant investigation that is pursued now to better present the indirect Z-source matrix converter as an attractive alternative for ac-ac buck-boost energy conversion. Findings presented here on have already been verified in simulation or experimentally using a laboratory-constructed prototype.