The present application provides (in addition to more broadly applicable inventions) improvements which are particularly applicable to two-sided power semiconductor devices which use bipolar conduction. In this class of devices, the inventor has realized that two or three of the four (or more) semiconductor doping components which form the carrier-emission structures and control structures in the active device (array) portion of a two-sided power device can also be used, with surprising advantages, to form field-limiting rings around the active arrays on both surfaces. Most preferably, in some but not necessarily all embodiments, a shallow implant of one conductivity type is used to counterdope the surface of a well having the other conductivity type. This shallow implant, singly or in combination with another shallow implant of the same conductivity type, works to shield the well from the effects of excess charge at or above the surface of the semiconductor material.