Using hospital discharge abstract data for fiscal year 1984 for all acute-care hospitals treating Medicare patients, the authors measured four mortality rates: inpatient deaths, deaths within 30 days of discharge, and deaths within two fixed periods following admission (30 days, and the 95th percentile length of stay for each condition). The metric of interest was the probability that a hospital would have as many deaths as it did (taking age, race, and sex into account). Differences among hospitals in inpatient death rates were large and significant for 22 of 48 specific conditions studied and for all conditions together. The authors compared pairs of conditions in terms of hospital rankings by probability of observed numbers of inpatient deaths; they found relatively low correlations for most comparisons except between a few surgical conditions. When they compared different pairs of the four death measures, the correlations were moderate to high. Data on hospital death rates cannot now be used to draw inferences about quality of care. The magnitude of variability in death rates, however, argues for further study of hospital death rates.