Consider a life testing experiment consisting ofnitems, (n– 1) of which have the same expected life while one of them could have a much longer expected life. The standard estimators based on a homogeneous model if used in such a case, would tend to overestimate and result in a large mean squared error (MSE). The present paper considers (n– 1) items having p.d.f. given by l/σ exp (–x/σ) while the remaining one has p.d.f. α/σ exp (–xα/σ), 0 < < 1. We consider estimators of c by linear combinations of the first few order statistics. An optimal estimator is suggested and its MSE is compared with that of the standard estimators. The cases ofn= 3 and 4 are explicitly evaluated.