Let $Pi_i, cdots, Pi_k$ denote k gamma distributions with a common known shape parameter (degrees of freedom) r and scale parameters $ heta_1, cdots, heta_k$, respectively. Kim proposed an improved lower bound LB$(delta^*)$, which concerns a two-stage elimimation type procedure for selecting the population associated with the largest scale parameter $max_{1leqileqk} heta_i$. The design constants (nr, mr, c) are given for k=4(1)10, $p^*=.95,.90 and delta^*=1.75,2.0$. With these design constants, a comparison study was made with the procedure of Lee and Choi. As can be seen from the table, these are moderate amount of savings in the expected total sample size. Thus, together with the result in Lee and Choi, the two-stage procedure can perform much better than a single stage procedure.