The accretionary histories recorded along the convergent margins in southwest Alaska and southwest Japan are punctuated by two anomalous events: near-trench magmatism closely associated in time and space with landward structural vergence. In both areas, the near-trench magmatism is believed to be related to the subduction of an active spreading center. It is postulated that these anomalous thermal events caused the backstop (i.e., mechanical boundary) within the prism to be reoriented to a seaward instead of a landward dip. This seaward-dipping backstop resulted in the development of landward-verging structures, for the only time in the almost 100-m.y. history of these two margins. A modern analog may be the Washington convergent margin. These examples illustrate the potential importance of thermal history and the dip of the backstop in controlling the style of accretion in submarine wedges.