In the eastern Aleutian arc, western Sumatra, and southwestern Japan, the distribution of igneous rocks cannot be explained by direct analogy with the igneous activity in modern island arcs. In these places, episodes of intrusion occurred within the accretionary prism, anomalously close to an active trench. For the eastern Aleutian arc and Sumatra, we speculate that the near-trench igneous rocks could be related to the subduction of a ridge that trended nearly perpendicular to the trench. The ridge-trench-trench triple junction so formed migrated along the trench. As the accretionary prism was under-thrust by the ridge, it would increase the heat flow sufficiently to cause partial melting of the sediment. In Japan, the near-trench igneous rocks could be related to the migration of a trench-trench-trench triple junction along the Japan Trench. The activity associated with this triple junction may be continuing today.