We present a compilation of high time-resolution photometric observations of quiescent soft X-ray transients obtained with the Acquisition Camera on Gemini-South. A0620-00 (V616 Mon) was observed with a short cycle time and high precision. Superimposed on the ellipsoidal modulation we find several prominent flares together with weaker continual variability. The flares seen sample a shorter time-scale than those reported in previous observations, with rise times as low as 30 s or less; most flares show unresolved peaks. The power density spectrum (PDS) of A0620-00 appears to exhibit band-limited noise closely resembling the X-ray PDS of black hole candidates in their low states, but with the low-frequency break at a lower frequency. X-ray Nova Muscae 1991 (XN Mus 1991, GU Mus) shows much larger-amplitude flares than A0620-00, and if a break is present it is at a lower frequency. X-ray Nova Velorum 1993 (XN Vel 1993, MM Vel) shows very little flaring and is, like A0620-00, dominated by the ellipsoidal modulation. We discuss the possible origins for the flares. They are clearly associated with the accretion flow rather than an active companion, but whether they originate in the outer disc, or are driven by events in the inner region, is not yet resolved. The similarities of the PDS to those of low/hard-state sources would support the latter interpretation, and the low break frequency is as would be expected if this frequency approximately scales with the size of an inner evaporated region. We also report the discovery of a new variable star only 14 arcsec from XN Mus 1991. This appears to be a W UMa star, with an orbital period of about 6 h.