In this paper we study the performance of bufferless optical WDM packet switching networks with various wavelength conversion degrees. We first introduce an optimal scheduling algorithm that maximizes the network throughput in this type of network. We then derive a novel analytical model to evaluate the network performance in terms of packet loss probability under the scheduling algorithm for Bernoulli traffic. Our model is the first accurate analytical model for bufferless WDM packet switching with variable conversion degrees and can be used to quantitatively determine the minimum wavelength conversion degree required for a certain traffic load. We also conducted simulations to validate the analytical model. Both the analytical and simulation results reveal that limited range wavelength conversion can achieve almost the same network performance as full wavelength conversion.