Equipping all nodes of a large optical network with full conversion capability is prohibitively costly. To improve performance at reduced cost, sparse converter placement algorithms are used to select a subset of nodes for full-conversion deployment. Further cost reduction can be obtained by deploying only limited conversion capability in the selected nodes. We present a limited wavelength converter placement algorithm based on the k-minimum dominating set (k-MDS) concept. We propose three different cost-effective optical switch designs using the technologically feasible nontunable optical multiplexers. These three switch designs are flexible node sharing, strict node sharing, and static mapping. Compared to the full search heuristic of O(N3) complexity based on ranking nodes by blocking percentages, our algorithm not only has a better time complexity O(RN2), where R is the number of disjoint sets provided by k-MDS, but also avoids the local minimum problem. The performance benefit of our algorithm is demonstrated by network simulation with the U.S Long Haul topology having 28 nodes (R is 5) and the National Science Foundation (NSF) network having 16 nodes (R is 4). Our simulation considers the case when the traffic is not uniformly distributed between node pairs in the network using a weighted placement approach, referred to as k-WMDS. From the optical network management point of view, our results also show that the limited conversion capability can achieve performance very close to that of the full conversion capability, while not only decreasing the optical switch cost but also enhancing its fault tolerance.