The problem of selecting the best population in the case of complete data when the underlying distributions are normal and two parameters exponential distribution has been discussed by Gupta and Sobel (1958), and Guttman (1961). In the present work certain population problems will be considered when the data are censored above and the underlying distribution is exponential with two parameters, for which, we shall discuss various cases by stating the procedure and give the proof that the procedure is parameter free.