In distilling Einstein-Podolsky-Rosen (EPR) pairs from three-party states, the optimal distillation rate for obtaining entanglement between a specified pair of parties has been previously shown to be the asymptotic entanglement of assistance. We have demonstrated a protocol for W and W-like three-party states in which higher overall distillation rates may be achieved at the cost of the bipartite entanglement obtained being shared between random pairs of parties. We have further derived various bounds on the distillation rate for the states in question.
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