Disclosed are semiconductor die packages having overlapping dice, systems that use such packages, and methods of making such packages. An exemplary die package comprises a leadframe, a first semiconductor die, and a second semiconductor die that has a recessed portion in one of its surfaces. The first die is disposed over a first portion of the leadframe, and the second die is disposed over a second portion of the leadframe with its recess portion overlying at least a portion of the first die. Another exemplary die package comprises a leadframe with a recessed area, a first semiconductor die disposed in the recessed area, and a second semiconductor die overlying at least a portion of the first die. Preferably, electrically conductive regions of both dice are electrically coupled to a conductive region of the leadframe to provide an interconnection between dice that has very low parasitic capacitance and inductance.