Two auctions have been proposed in the literature for siting noxious facilities: the high-bid and the low-bid auctions. In this paper, we pursue the analysis of these auctions made by O'Sullivan (1993), where he concludes that the high-bid auction has the edge over the low-bid auction. We point out that O'Sullivan has made an approximation for the expected value of the compensation obtained with the high-bid auction, and we show how to obtain the exact value. We discuss a paradox linked with O'Sullivan's result, which mitigates his conclusions, and we show that with exact compensation, the high-bid auction mechanism is indeed far superior to the low-bid auction.