Summary: One of the most exciting prospects for the LISA gravitational wave observatory is the detection of gravitational radiation from the inspiral of a compact object into a supermassive black hole. The large inspiral parameter space and low amplitude of the signal make detection of these sources computationally challenging. We outline here a first-cut data analysis scheme that assumes realistic computational resources. In the context of this scheme, we estimate the signal-to-noise ratio that a source requires to pass our thresholds and be detected. Combining this with an estimate of the population of sources in the universe, we estimate the number of inspiral events that LISA could detect. The preliminary results are very encouraging—with the baseline design, LISA can see inspirals out to a redshift \(z = 1\) and should detect over a thousand events during the mission lifetime.