Abstract: A concrete-finishing machine has a drive horse, a slave horse, and a bridge-like truss selectively connectable to, or separable from, those horses at different levels so those horses can roll along surfaces at the same level or at distinctly-different levels. Vertically-directed jacks can dispose a screed or a float at different distances below the level of the bridge-like truss, and that screed and that float can be shifted along the length of that bridge-like truss to avoid obstructions within the area to be concreted. Those jacks can set different sections of the screed at different levels and thereafter simultaneously move all sections of that screed up or down. Interacting surfaces on the jacks and on the bridge-like truss enable those jacks to be readily secured to or separated from that bridge-like truss.