In WDM All-optical networks, the deployment of wavelength converters improves the blocking performance. One solution is to equip every node in the network with converters (full wavelength conversion); however the cost and the technological limitations make it not practical. The alternative is to choose a subset of nodes and equip them with wavelength converters (sparse wavelength conversion). This paper makes the first known attempt to solve the sparse wavelength converters placement problem using the k-Weighted Minimum Dominating Set (k-WMDS) approach. To evaluate our proposed scheme under Non-uniform traffic, we compared it against the well-known approach (referred to as k-BLK) of placing converters in nodes having the highest blocking percentage. The two algorithms were compared under different Non-uniform traffic loads using network simulation with the U.S Long Haul and NSFNET topologies. For different values of the hop-distance parameter, k, the proposed k-WMDS algorithm has consistently given better blocking performance than k-BLK under the constraint that the number of converters in both algorithms is equal to the cardinality of the k-weighted minimum dominating set.