The microtubule cytoskeleton and the mitotic spindle are highly dynamic structures1, yet their sizes are remarkably constant, thus indicating that the growth and shrinkage of their constituent microtubules are finely balanced2,3. This balance is achieved, in part, through kinesin-8 proteins (such as Kip3p in budding yeast and KLP67A in Drosophila) that destabilize microtubules3-8. Here, we directly demonstrate that Kip3p destabilizes microtubules by depolymerizing them - accounting for the effects of kinesin-8 perturbations on microtubule and spindle length observed in fungi and metazoan cells. Furthermore, using single-molecule microscopy assays9, we show that Kip3p has several properties that distinguish it from other depolymerizing kinesins, such as the kinesin-13 MCAK10,11. First, Kip3p disassembles microtubules exclusively at the plus end and second, remarkably, Kip3p depolymerizes longer microtubules faster than shorter ones. These properties are consequences of Kip3p being a highly processive, plus-end-directed motor12, both in vitro and in vivo. Length-dependent depolymerization provides a new mechanism for controlling the lengths of subcellular structures13.