The problem of estimating regression parameters in an exponential model with censoring is considered when it is a priori suspected that the parameters may be restricted to a subspace. James-Stein(JS)type of estimators is obtained which dominates the usual maximum likelihood(ml)estimators. The relative performance of the JS type estimators is compared to the ml estimators using quadratic distributional risk under local alternatives. It is demonstrated that the JS type estimators are asymptotically superior to the usual ml estimators. Further, it is shown that the JS type estimator is dominated by its truncated part.