Recent years have seen the advent of energy conservation as a key engineering and scientific challenge of our time. At the same time, most IP networks are typically provisioned to 30%-40% average utilization, leading to a significant waste of energy. Current approaches for creating more frugal networks rely on instantaneous and global knowledge of the traffic matrix and network congestion levels - a requirement that can be impractical for many network operators. We introduce a new traffic-agnostic metric for quantifying the quality of a frugal topology, the Adequacy Index (ADI).We show that the problem of minimizing the power consumption of a network subject to a given ADI threshold is NP-hard and present two polynomial time heuristics - ABStAIn and CuTBAck. We perform extensive simulations using topologies and traffic matrices from 3 real networks. Our results show that ABStAIn and CuTBAck are as effective as an exponential time traffic based solution at creating frugal topologies and outperform a state of the art polynomial time traffic based solution by about 80%. Furthermore, the median link utilization observed with ABStAIn and CuTBAck is similar to that with traffic based solutions, with the maximum link utilization never exceeding 80%.