One aspect of the invention pertains to a semiconductor die with rounded sidewall junction edge corners. Such rounding reduces stress accumulations at those corners. In other embodiments of the invention, the sharpness of other corners and edges in the die are reduced. For example, reducing the sharpness of the bottom edge corners formed by the intersection of a sidewall and the back surface of a die can further diminish stress accumulations. One embodiment pertains to a wafer carried on a wafer support, where the wafer includes a multiplicity of such dice. Another embodiment involves a semiconductor package containing such dice. Methods of fabricating the dice are also described.