Optical burst switching (OBS) is an experimental network technology that enables the construction of very high capacity routers, using optical data paths and electronic control. In this paper, we study two designs for wavelength converting switches that are suitable for use in optical burst switching systems and evaluate their performance. Both designs use tunable lasers to implement wavelength conversion. One is a strictly nonblocking design, that also requires optical crossbars. The second substitutes wavelength grating routers (WGR) for the optical crossbars, reducing cost, but introducing some potential for blocking. We show how the routing problem for the WGR-based switches can be formulated as a combinatorial puzzle or game, in which the design of the game board corresponds to the pattern of interconnections used to join the input sections of the switch to the output sections. We use this to show how the interconnection pattern affects the performance of the switch, and to facilitate the design of interconnection patterns that yield the best performance. Our results show that for a typical switch configuration, the WGR-based design can deliver more than 87% of the throughput of a fully nonblocking switch.