In this paper, we discuss two-stage procedures for selecting the largest location parameter among k (≥ 2) negative exponential populations having unknown and unequal scale parameters. We compare this new two-stage procedure for k = 2 with that of Mukhopadhyay (1984), and Mukhopadhyay's (1984) procedure comes out as the inferior one. To facilitate this comparison, we need a specialized table (Table I) for the Studentized smaller Chi-squares, and we provide with an exact method to do just that. The Table I is also very useful for another related problem discussed in Mukhopadhyay and Hamdy (1963). In the end, we present a limited simulation study about the moderate sample-size performances of the two-stage procedures in Mukhopadhyay (1984), and Mukhopadhyay and Hamdy (1983) for k = 2. However, for a general k (≥ 3), our newly developed two-stage procedures as developed here are the only ones known to us at this time.