The problem of component wise estimation of ordered location parametersθ1(θ1≤θ2) of two independent exponential distributions is investigated. The scale parameters are assumed to be unequal but known. Independent random samples of unequal sample sizes are drawn from two populations and the estimators admissible among the mixed estimators ofθ1andθ2are obtained. It is shown that the minimum risk estimators (MREs) ofθ1andθ2without assumingθ1≤θ2are inadmissible when one does assume thatθ1≤θ2. The efficiencies of mixed estimators relative to MREs (without assumingθ1≤θ2) are tabulated for equal sample sizes and equal scale parameters.