A combustor for an industrial turbine includes a single transition piece transitioning directly from a combustor head-end to a turbine inlet. The transition piece includes an inner surface and an outer surface. The inner surface bounds an interior space for combusted gas flow from the combustor head-end to the turbine inlet. The outer surface at least partially defines an area for compressor discharge air flow. The transition piece includes a plurality of apertures configured to allow compressor discharge air flow into the interior space. Each of the plurality of apertures extends from an entry portion on the outer surface to an exit portion on the inner surface.