Within the framework of three-neutrino and four-neutrino scenarios that can describe the results of the LSND experiment, we consider the capabilities of short-baseline neutrino oscillation experiments at a neutrino factory. We find that, when short-baseline (L less than or similar to 100 km) neutrino factory measurements are used together with other accelerator-based oscillation results, the complete three-neutrino parameter space can best be determined by measuring the rate of v(e) --> v(tau) oscillations, and measuring CP violation with either v(e) --> v(mu) or v(mu) --> v(tau) oscillations (including the corresponding antineutrino channels). With measurements of CP violation in both v(e) --> v(mu) and v(mu) --> v(tau) it may be possible to distinguish between the three- and four-neutrino cases.