  We consider entanglement distillation from a single-copy of a multipartite
state, and instead of rates we analyze the "quality" of the distilled
entanglement. This "quality" is quantified by the fidelity with the GHZ-state.
We show that each not fully-separable state $\sigma$ can increase the "quality"
of the entanglement distilled from other states, no matter how weakly entangled
is $\sigma$. We also generalize this to the case where the goal is distilling
states different than the GHZ. These results provide new insights on the
geometry of the set of separable states and its dual (the set of entanglement
witnesses).
