An inverted pyramid multi-die package provides, for each die pad on an upper die, a rigid support underneath extending to a substrate. Such configuration reduces both the wire sweep and weakening torques. A lower die, smaller than the upper die in at least one dimension, may be positioned between the upper die and the substrate. The two dice may or may not contact each other, or they may contact each other via an intermediate spacer. The lower die may be a flip chip. The multi-die package may be fashioned without the lower die or the substrate. Wire sweep is reduced, because the second die is smaller than the upper die in at least one dimension. Weakening torques are reduced, because spacers at the periphery of the upper die absorb the impact of bonding wires thereon.