We previously described coronal events that originate in the 2-6 R field of view of the LASCO white-light coronagraph and involve the simultaneous ejection of material inward toward the Sun and outward away from it. Now, in a study of more than 160 in/out pairs, we have found that these features are density enhancements at the leading and trailing edges of depletions that occur when slowly rising coronal structures separate from the Sun. The outward component is shaped like a large arch with both ends attached to the Sun, and the inward component is often resolved into loops. We also found about 60 additional events in which the outward components began near the edge of the occulting disk and inward components were not visible, as if these events were in/out pairs that originated below the 2 R radius of the occulting disk. We conclude that in/out pairs belong to a broad class of streamer detachments, which include "streamer blowout" coronal mass ejections, and we suppose that all of these events occur when rising magnetic loops reconnect to produce an outgoing helical flux rope and an ingoing arcade of collapsing loops.