Among the several architectures for IP (Internet Protocol) over WDM networks, one promising approach is to overlay a logical topology that consists of lightpaths on the physical WDM network, such that each lightpath carries IP traffic between edge nodes. Many of the conventional methods for designing the logical topology deal with the case of a constant number of wavelengths being available on each fiber. While the number of wavelengths offered by current optical technology is now of the order of thousands, it is not necessary to utilize all wavelengths on each fiber in building an effective logical topology on a WDM network. Instead,.several wavebands may be considered for introduction by deploying. optical fiber amplifiers when additional wavelengths are actually required. In this case, the number of available wavelengths on the respective fibers depends on the number of optical fiber amplifiers deployed on each fiber. In this paper, we propose a new heuristic algorithm for the design of a logical topology with as few optical fiber amplifiers as possible, so that the approach is cost-effective. We then compare our proposal with conventional methods in terms of average packet delays and throughput, and show that our algorithm reduces the number of optical fiber amplifiers required. We also investigate the effect of increasing the number of wavelengths multiplexed on each fiber, by assuming that the product of the number of available wavelengths and the bandwidth of each wavelength is constant. The results show that such a logical topology is able to accommodate a greater volume of traffic by multiplexing more wavelengths on each fiber. The approach thus conforms to Cao's Law.