Time Sliced Optical Burst Switching is a proposed variant of optical burst switching, in which switching is done in the time domain, rather than the wavelength domain. This eliminates the need for wavelength converters, the largest single cost component of systems that switch in the wavelength domain. We examine some of the key design issues for routers that implement time sliced optical packet switching. In particular, we focus on the design of the Optical Time Slot Interchangers (OTSIs) needed to effect the required time domain switching. We introduce a novel nonblocking OTSI design and also show how blocking OTSIs can be used to implement the required switching operations. We study the performance of systems using blocking OTSIs and demonstrate that near ideal statistical multiplexing performance can be achieved using even quite inexpensive, blocking OTSI designs. These results suggest that optical technology may one day be able to provide a cost-effective alternative to electronics in packet switching systems.