The power and procurement cost of bandwidth in system-wide networks has forced a steady drop in the byte/flop ratio. This trend of computation becoming faster relative to the network is expected to hold. In this paper, we explore how cost-oriented task placement enables reducing the cost of system-wide networks by enabling high performance even on tapered topologies where more bandwidth is provisioned at lower levels. We describe APHiD, an efficient hierarchical placement algorithm that uses new techniques to improve the quality of heuristic solutions and reduces the demand on high-level, expensive bandwidth in hierarchical topologies. We apply APHiD to a tapered fat-tree, demonstrating that APHiD maintains application scalability even for severely tapered network configurations. Using simulation, we show that for tapered networks APHiD improves performance by more than 50% over random placement and even 15% in some cases over costlier, state-of-the-art placement algorithms.