In this paper we consider a Digital Subscriber Line (DSL) system with N orthogonal narrowband tones. Each user has a limited power budget, and our goal is to determine the power allocation of each user that enables the 'user capacity' of the system to be approached. In this paper, we use 'user capacity' to denote the maximum number of users that can be supported by the system, provided that each user is guaranteed to have a data rate that lies within a prescribed range. Finding a power allocation that enables this capacity to be approached directly can be quite cumbersome because it involves solving a (non-convex) integer-program. In order to circumvent this difficulty, in this paper we propose an alternate approach that is based on exploiting the fairness and per-tone convexity of the harmonic meanrate objective. Using these features, we devise a computationallyefficient power allocation technique that enables the user capacity of the DSL system to be approached more closely than power allocation techniques that are more computationally demanding.