We investigate the rupture process of a sequence of repeating Mw 2.1 earthquakes on the San Andreas Fault in Parkfield spanning the occurrence of the September 28, 2004 mainshock by inverting seismic moment rate functions obtained from empirical Green's function deconvolution. The results show that these events have extremely concentrated slip patches with radii on the order of 10–20 m, with peak slip between 8.4 and 11.4 cm. The rupture speed and rise time are consistent with values of larger earthquakes. The spatial distribution of stress drop for the events shows low average values 2.5–5.6 MPa and very large peak values of 66.7–93.9 MPa. The results show that strong asperities can exist at small scales on an otherwise weak fault, and helps reconcile differences between traditional spectra-based and tectonic loading methods for determining the stress drop of small repeating earthquakes.