We consider the problem of optimally placing a given number of wavelength converters on a path to minimize the call blocking probability. Using a simple performance model, we first prove that uniform spacing of converters is optimal for the end-to-end performance when the link loads are uniform and statistically independent. We then show that significant gains are achievable with optimal placement compared to random placement. For non-uniform link loads, we provide a dynamic programming algorithm for the optimal placement and compare the performance with random and uniform placement. Optimal solutions for bus and ring topologies are also presented.