The gravitational waves produced during the inspiral of a compact body into a supermassive black hole provide a map of the spacetime geometry near the black hole. The detection of such sources is a key science driver motivating the specification of LISA. The inspiral parameter space is too large to allow detection using fully coherent matched filtering. Instead, data analysis will involve a mixed coherent/incoherent hierarchical search, which will start with a coherent search of short segments of the data. We present tentative results from scoping out the data analysis issues. We give estimate the number of templates required in the first stage of the search the maximum length of the segments in the coherent stage given realistic computational resources. From this we deduce the loss in optimal signal to noise using the hierarchical scheme. Finally, we present preliminary estimates of detection rates and the implications for the design of LISA.