In this paper, we study distributed power control in an interference network. In particular, distributed power control mechanisms are devised by exploiting a one-shot noncooperative game based on a suitably chosen utility function. The utility is a function of quality of service (QoS) objectives defined in terms of fading-induced outage probabilities. Equilibrium analysis of the resulting power control game is made, and its relationship with admission control is discussed. The main contribution of the paper is a mechanism for obtaining smooth non-monotonic reaction curves, in contrast to sharp cut-offs with increasing interference that are characteristic of admission control. This is done via the introduction of a factor f(d)(.) into the utility function, allowing users to smoothly decrease their objectives in response to interference. The resulting algorithm is called non-monotonic power control (NMPC). We provide sufficient conditions for a unique Nash equilibrium (NE) under NMPC. The equilibria are studied in numerical examples, which exhibit that NMPC increases the number of users who achieve their objectives, without removing any user, as compared to previous utility-based power control algorithms with harsher reaction curves. Considerable energy efficiency is gained by a transfer of resources from the disadvantaged user to the advantaged: users whose SIR objectives are infeasible under current channel gains reduce their own transmit power thus helping on others. We view this solution as an attractive alternative to pricing in wireless networks formed by cooperative nodes (such as sensor networks) where an economic model is not natural.