Recent observations show marked acceleration and thinning of tributary ice streams following shrinkage or loss of a few of the many small ice shelves that ring Antarctica and Greenland. Our model experiments, which adopt a simplified geometry, show that calving from or partial disintegration of a small ice shelf has more effect on tributary ice streams than does loss of a berg of equal length from a larger ice shelf. Our results, which are consistent with the recent observations, indicate that even small ice shelves can provide important restraint on tributary flow from ice sheets, implying that characterization and modeling of the full range of ice shelves will be required for accurate projection of ice-sheet changes and their influence on sea level.