The entropy, or amount of uncertainty, of a diagnostic hypothesis is defined and used to compute the possible hypothesis improvement when each unperformed test is assumed to be executed. This criterion permits objectively ranking such tests to guide the physician in making his next choice, to actually refine the current hypothesis. The procedure can be recurrently applied until the entropy of the diagnostic hypothesis is reduced, or the hypothesis improved, to a medically acceptable level. The method has been specified for a group of five trisomies, including Mongolism, and 100 patients have been diagnosed from their records; those results are discussed. A computer realization is briefly presented, and improvements are proposed.ETX