Some published modifications of the Poisson distribution for describing IC yield are critiqued. It is shown that it is incorrect to obtain an average yield for a non-uniform defect population by integrating, either in the geometrical space or in the density space, the Poisson distribution with some assumed density distribution functions. The correct way, and happily also the simplest way, is to average the yields of regionally partitioned subpopulations in a discrete manner. The simple Poisson distribution would become rigorously correct when the size of an imaginary IC increases to one quarter of a wafer, regardless of the non-uniformity in defect density. It is also shown that both cases of clustering of defects, one due to interaction among defects themselves, and the other due to wafer regional preference, result in increased yield for a given defect density in a wafer. On the other hand when there are interactions between defects and IC active area elements, or when defects themselves have physical dimensions, there would be a decreased yield for a given defect density, and a non-zero intercept in the plot of the logarithm of yield vs the active device area.