Since the start of the SOHO mission three years ago, the Large Angle Spectrometric Coronagraph (LASCO) has recorded numerous examples of small, faint features moving inward through the corona. The inflows are observed at heliocentric distances of 2--4 RS and became increasingly common during 1998, as solar and coronal mass ejection (CME) activity increased. The inward-moving structures, which are most easily detected in running difference movies, often have a cusplike appearance and tend to leave a density depletion in their wake; the downward velocities range from less than 20 km s-1 to over 100 km s-1. The downflows are observed typically ~1 day after the passage of a CME, and coexist side by side with continuing outflows of streamer material. We interpret these small-scale events as observational signatures of the gradual closing-down of magnetic flux dragged outward by CMEs or other transient outflows. ¿ 1999 American Geophysical Union