Heavy ion driven inertial fusion drivers and experiments use space-charge dominated beams that require longitudinal bunch compression to increase the power delivered on target. In these scenarios, a drift compression section is designed such that the longitudinal compression stagnates as a result of the space charge repulsion of the beam. Special attention is given to keeping all parts of the beam matched, which is not trivial since the rate of current increase varies along the beam. A conceptual drift compression section was designed for a space-charge dominated beam. It will be shown that all parts of the beam can be kept approximately matched.