A structure including a first semiconductor chip with front and rear surfaces and a cavity in the rear surface. A second semiconductor chip is mounted within the cavity. The first chip may have vias extending from the cavity to the front surface and via conductors within these vias serving to connect the additional microelectronic element to the active elements of the first chip. The structure may have a volume comparable to that of the first chip alone and yet provide the functionality of a multi-chip assembly. A composite chip incorporating a body and a layer of semiconductor material mounted on a front surface of the body similarly may have a cavity extending into the body from the rear surface and may have an additional microelectronic element mounted in such cavity.