Many split-mouth trials are characterized by the pairing of site-specific outcome and baseline data within each segment of a subject's mouth. However when the response variable of interest is binary, methods of statistical analysis for this design are not well developed. In this paper we present several analytic approaches that may be taken to the resulting data, showing how the efficiency of statistical inferences can be improved by appropriately incorporating the baseline information. The advantages and disadvantages of the different approaches are discussed in the context of an example from the published literature. The results from a limited simulation study are also presented.