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Sparse wavelength conversion and an appropriate routing and wavelength assignment (RWA) algorithm are two key factors in improving the blocking performance in wavelength-routed all-optical networks. It has been shown that the optimal placement of a limited number of wavelength converters in an arbitrary mesh network is an NP complete problem. Various heuristic algorithms have been proposed in which most assume that a static routing and random wavelength assignment algorithm is employed. However, existing works show that dynamic RWA algorithms can achieve significantly better performance. Our study further demonstrates that wavelength converter placement and RWA algorithms are closely related in that a well designed wavelength converter placement mechanism for a particular RWA algorithm might not work well with a different RWA algorithm. Our objective is to investigate wavelength converter placement under dynamic routing algorithms. Specifically, we propose a heuristic algorithm called weighted maximum segment length (WMSL) algorithm for limited wavelength converter placement for arbitrary mesh networks under a dynamic RWA algorithm adopting least-loaded routing and first-fit wavelength assignment. The objective is to minimize the average blocking probability. Extensive simulation studies have been carried out over three typical mesh networks, including the 14-node NSFNET, 19-node EON and 38-node CTNET. We observe that the proposed WMSL algorithm not only outperforms existing wavelength converter placement algorithms by a large margin, but it can also achieve almost the same performance compared with full wavelength conversion under the same RWA algorithm.