Using less wavelengths to serve more communication channels is one of the primary goals in the design of WDM networks. By installing wavelength converters at some nodes in a network, the number of wavelengths needed can be reduced. It has been observed that the more converters installed in a network, the less number of wavelengths is needed, given the same network load. In this paper, we study the relationship between the number of converters and the number of wavelengths needed in a system, and propose a suite of theories and results on how to place the minimal number of converters in the system so that the number of wavelengths W is at most a constant α times the maximal link load L (i.e., W α L), where α = 3/2 or 5/3. The results show a significant saving of converters in networks of both special topologies and general topology.