Most zooarchaeologists employ some type of derived measure of skeletal element abundance in their analyses of faunal data. The minimum number of individuals (MNI) and the minimum number of animal units (MAU) are two of the most popular derived measurements, and each is based on a prior estimate of the minimum number of elements (MNE). Thus, the estimate of MNE from fragmented faunal fragments is the essential foundation for all inferences emanating from MNI and MAU estimates of skeletal element abundance. Estimating the MNE represented by a sample of faunal fragments is a complicated procedure that involves various assumptions, possible mathematical manipulations, and subjectivity. Unfortunately, the reasoning and methods underlying this procedure are unstandardized in zooarchaeology, and even worse, rarely made explicit. We review the scarce literature on this topic and identify two different approaches: the fraction summation approach and the overlap approach. We identify strengths and weaknesses in both approaches. We then present a new method that is based on using image-analysis GIS software to count overlapping fragments that have been converted to pixel images. This method maintains the strengths of the other methods while overcoming most of their weaknesses. It promises numerous powerful analytical capabilities that go far beyond the routines available in spreadsheets and databases. It also offers nearly boundless flexibility in database recoding and extremely complete information storage. Perhaps its greatest strength is that it is based on very intuitive reasoning.