We used remotely sensed data and a numerical model to study the processes controlling the stability of two rapidly changing ice shelves in West Antarctica. Both these ice shelves have been losing mass since at least 1996, primarily as a result of ocean-forced melt. We find that this imbalance likely results from changes initiated around 1970 or earlier. Our results also show that the shelves’ differing speedup is controlled by the strength of their margins and their grounding-line positions.