The determination of the "optimum pit limit" of a mine has long been considered as a fundamental problem of mine planning. A number of mathematical techniques have been proposed to solve this problem some of the more elaborate ones posing considerable computational difficulties for their implementation. Barnes and Johnson recently introduced "bounding techniques" to ease the computational effort required for determining the optimum pit. The aim of this paper is to point out and correct some errors in their techniques. A presentation of a general bounding algorithm is given.