In recent years, economists have come to recognize that the competition to obtain monopoly rents, i.e., rent seeking, may consume resources whose value greatly exceeds that associated with traditionally measured deadweight welfare loss triangles (Toilison, 1982). Early articles by Tullock (1967), Krueger (1974), and Posner 0975) all concluded that this competition would exactly dissipate the rents sought. Later articles by Tullock (1980) and Baysinger and Tollison 0980) modified that original conclusion. The present paper develops a model which raises further doubts about the complete transformation of rents into costs. The emphasis of the analytical framework presented is on the implications of the fact that rent seekers may typically be uncertain about being able to maintain a monopoly position even if they are initially successful in attaining one. It is demonstrated that when there is even a moderate level of uncertainty about retention, the likely effect will be a relatively large reduction in the magnitude of resources invested in rent seeking activities. In addition, it is shown that the size of this waste of resources depends somewhat on the extent to which rent seeking opportunities involve once and for all transfers as opposed to flows of rents. Finally, in those cases where a flow of rents is at stake, it is shown that considerable social waste might be eliminated through institutional changes which would reduce the subjective probabilities of potential monopolists retaining their rent streams once attained.