(In, Ga)N nanostructures show great promise as the basis for next generation LED lighting technology, for they offer the possibility of directly converting electrical energy into light of any visible wavelength without the use of down-converting phosphors. In this paper, three-dimensional computation of the spatial distribution of the mechanical and electrical equilibrium in nanoheterostructures of arbitrary topologies is used to elucidate the complex interactions between geometry, epitaxial strain, remnant polarization, and piezoelectric and dielectric contributions to the self-induced internal electric fields. For a specific geometry-nanorods with pyramidal caps-we demonstrate that by tuning the quantum well to cladding layer thickness ratio, h(w)/h(c), a minimal built-in electric field can be experimentally realized and canceled, in the limit of h(w)/h(c) = 1.28, for large h(c) values.