Resonant elastic scattering from InAs quantum dots (QDs) is studied by heterodyne spectroscopy. We show theoretically that heterodyne spectroscopy of a two-level quantum emitter is not sensitive to the inelastic fluorescence component. In practice, we easily measure the elastic emission even when the fluorescence is dominated by inelastic scattering. We are able to distinguish the resonant elastic fluorescence from a large background of scattered pump light by modulating the QD transition frequency with a surface acoustic wave. The signal linewidth is 250 Hz, limited by vibration-induced phase noise in the optical fibers used for resonant optical drive and fluorescence collection. (C) 2013 AIP Publishing LLC.