The process of diagnosis by elimination in terms of probabilities was analyzed mathematically. A piece of evidence which was only associated with a small number of differential diagnoses was of particular importance. To deal with a differential diagnosis, a feature is required which occurs commonly in a postulated diagnosis but rarely in its rivals, irrespective of its frequency in those already discriminated against. By using this analysis, inadequate evidence may be identified, new tests developed and their effectiveness assessed in a logical and efficient way. The approach was illustrated by considering the differential diagnosis of localized right lower quadrant abdominal pain.