stacked semiconductor assemblies in which a device such as a die, or a package, or a heat spreader is stacked over a first wire-bonded die. An adhesive/spacer structure is situated between the first wire-bonded die and the device stacked over it, and the device has an electrically non-conductive surface facing the first wire-bonded die. That is, the first die is mounted active side upward on a first substrate and is electrically interconnected to the substrate by wire bonding; an adhesive/spacer structure is formed upon the active side of the first die; and a device such as a die or a package or a heat spreader, having an electrically nonconductive side, is mounted upon the adhesive/spacer structure with the electrically nonconductive side facing the first wire bonded die. The side of the device facing the first wire bonded die may be made electrically nonconductive by having an electrically insulating layer, such as a dielectric film adhesive. Also, methods for making the assemblies are disclosed.