Flexible circuitry is populated on one or both sides with integrated circuits (ICs) each of which ICs has an IC profile (height). A substantially flat, windowed fixture with a fixture profile less than the IC profiles of the ICs is applied over an IC-populated side of the flexible circuitry causing at least a part of the ICs to emerge from respective fixture windows. Material is removed simultaneously from that portion of the ICs that emerge from the windows to result in lower-profile ICs which, in a preferred embodiment exhibit profiles substantially coincident with the fixture profile established by the upper surface of the fixture. The method is used to advantage in devising circuit modules by disposing the flexible circuitry about a rigid substrate to form the circuit module with a low profile. Some embodiments use substrates that are windowed or have inset areas into which the lower profile CSPs may be set to reach profile requirements.