The mean residual life of a non negative random variable X with a finite mean is defined by M(t) = E[X - t | X > t] for t >= 0. A popular nonparametric model of aging is new better than used in expectation (NBUE), when M(t) <= M(0) for all t >= 0. The exponential distribution lies at the boundary. There is a large literature on testing exponentiality against NBUE alternatives. However, comparisons of tests have been made only for alternatives much stronger than NBUE. We show that a new Kolmogorov-Smirnov type test is much more powerful than its competitors in most cases.