The requirement of “zero defects” is rapidly finding its way as a “standard” of quality in numerous quarters. This phrase has great psychological appeal, and is often taken literally at all levels in an organization even though quality motivation may be the intention. It is common to believe that when zero defects are found in the sample, this must be the case for “all the rest” as well. In this paper the technical side of “zero defects” is examined. We look at the statistics of zero defects and show what is implied about lot or process quality when zero defects is the actual sample outcome. The focus is on attribute measurements and includes some special cases where a significant measurement error exists and cases where a Bayesian statistical analysis may be appropriate.