Integrated circuit device packages and substrates for making the packages are disclosed. One embodiment of a substrate includes a planar sheet of polyimide having a first surface, an opposite second surface, and apertures between the first and second surfaces. A planar metal die pad and planar metal are attached to the second surface of the polyimide sheet. The apertures in the polyimide sheet are juxtaposed to the leads. A package made using the substrate includes an integrated circuit device mounted above the first surface of the polyimide sheet opposite the die pad. Bond wires are connected between the integrated circuit device and the leads through the apertures in the polyimide sheet. An encapsulant material covers the first surface of the polyimide sheet, the integrated circuit device, the bond wires, and the apertures. The die pad and leads are exposed at an exterior surface of the package.