IfSandTare survival functions for two life distributions, thenSis said to be uniformly stochastically smaller thanT, denoted byS≪T, if θ(x) ≡S(x)/T(x) is nonincreasing inxon {x:T(x) > 0}. This ordering is transitive. Uniform stochastic ordering (USO) has found important applications in nonparametric accelerated life testing, among other areas. It has been shown that the nonparametric maximum likelihood estimator (NPMLE) ofSunder USO whenTis known is inconsistent. Dykstra, Kochar Robertson derived the restricted NPMLE's of several unknown survival functions linearly ordered by USO. This article shows that these too are inconsistent in general. Rojo and Samaniego gave excellent ad hoc estimators ofSandTwhen the other is known. Based on their idea for the one-sample problem, they gave two ad hoc estimators (one of them only implied) ofSandTwhen they are both unknown. These are consistent, but they lack some desirable properties. This article introduces a one-parameter family of estimators that contains both of these estimators as extreme members. Some heuristic arguments are given to show that an interior member of this family is the appropriate one to choose.