This chapter examines the problem of maximizing total utility subject to an upper bound on the range of utilities. It shows that this maximization problem, when solved subject only to budget and range constraints, is equivalent to the problem of maximizing the equity threshold social welfare function (described in Chap. 11) subject to a budget constraint and with the fairness parameter \(\Delta \) set equal to the desired maximum range. The solution is given in closed form and contains only two distinct utility levels, possibly with a third (intermediate) level assigned to a single stakeholder. The chapter also shows by counterexample that the problem is not regionally decomposable.