We have developed a new digital system mode of operation, refereed to as error-tolerance, the purpose of which is to increase effective yield. Errortolerance is based on the fact that many digital systems exhibit acceptable behavior even though they contain defects and occasionally output errors. A radically new test methodology, called intelligible testing, is required to support error-tolerance. This paper addresses parts of this methodology. There are several fundamental philosophical differences between intelligible testing and classical testing, such as: intelligible testing is application oriented; it partitions die and chips into multiple categories, not just good and bad parts; and it supplies quantitative information about the effects of defects on errors, i.e. it is error based rather than fault based. We describe three types of error attributes, namely error-rate, error-accumulation (retention), and errorsignificance. We present test techniques for estimating quantitative values for these qualitative attributes. Testing to support error-tolerance involves new ATPG tools, new fault simulators, and new DFT and BIST techniques.