The Cochran-Armitage test is frequently used to test for trends among binomial counts. The nonparametric order-restricted test is less common. We construct a Bayesian test for a trend which removes some restrictions associated with the Cochran-Armitage test and the order-restricted test We apply these tests to the Worcester Heart Attack Study to assess decreasing trends in case-fatality rates for patients hospitalized with acute myocardial infraction.