Asymptotic manipulations of entanglement can exhibit genuine irreversibility

It is commonly believed that distillation of entanglement fan be, in genera l, irreversible. Perhaps the strongest evidence is constituted by the exist ence of the bound entangled states. However, even a single example of state exhibiting this irreversibility has not been found so far. We show that fo r a family of states the process of distillation of entanglement is truly i rreversible. These states have a nonzero amount of bound entanglement and, at most, a very small amount of free entanglement.