A lifetime X with survival function S, mean residual life function (MRL) M, and finite mean μ is said to be new better than used in expectation (NBUE) if M(t)≤μ for all t≥0. We propose a new estimator for S, based on a natural estimator of M defined under the NBUE restriction. This is much simpler to implement than the only other restricted estimator in the literature. We also derive some asymptotic properties of the MRL of X and extend our results to the censored case.