Piezoelectric nanotransducers may offer key advantages in comparison with conventional piezoelectrics, including more choices for types of mechanical input, positions of the contacts, dimensionalities and shapes. However, since piezo-semiconductive nanostructures are generally much easier to fabricate and integrate into functional systems than insulating materials, modeling becomes significantly more intricate and the effects of free charges have been considered only in a few studies. The available reports are complicated by the absence of proper nomenclature and figures of merit. Besides, some analyses are incomplete. For instance, the local piezopotential and free charges within axially strained conical piezo-semiconductive nanowires have only been systematically investigated for very low doping (1016 cm-3) and under compression. Here we give the definitions for the enhancement, depletion, base and tip piezopotentials, their characteristic lengths and both the tip-to-base and the depletion-to-enhancement piezopotential-ratios. As an example, we use these definitions for analyzing the local piezopotential and free charges in n-type ZnO truncated conical nanostructures with different doping levels (intrinsic, 1016 cm-3, 1017 cm-3) for both axial compression and traction. The definitions and concepts presented here may offer insight for designing high performance piezosemiconductive nanotransducers.