We investigate the degree to which the built-in electric field can be suppressed by employing polarization-matched barriers in III-N quantum well and dot structures grown along the c axis. Our results show that it is possible to take advantage of the opposite contributions to the built-in potential arising from the different possible combinations of wurtzite GaN, InN, and AlN when alloying the materials. We show that, for a fixed bandgap of the dot/well, optimal alloy compositions can be found that minimize the built-in field across the structure. We discuss and study the impact of different material parameters on the results, including the influence of nonlinear effects in the piezoelectric polarization. Structures grown with unstrained barriers and on GaN epilayers are considered, including discussion of the effects of constraints such as strain limits and alloy miscibility.