Let M be a general mixed state of two spin-1/2 particles which could have resulted from the transmission of an initially pure singlet state ψ ψ − − = ( ↑ ↑ ↓ ↓ − − ↓ ↓ ↑ ↑ ) / 2 through a noisy channel between Alice and Bob, which will be used to distill some pure entanglement. The fidelity of M F = ⟨ ⟨ ψ ψ − − | M | ψ ψ − − ⟩ ⟩ is a convenient expression of its purity relative to a perfect singlet. Suppose that M is already a pure state of two particles M = | ϕ ϕ ⟩ ⟩ ⟨ ⟨ ϕ ϕ | for some ϕ ϕ . The entanglement for ϕ ϕ , as already established, is the von Neumann entropy E ( ϕ ϕ ) = S ( p A ) = S ( p B ) where p A = tr B ⁡ ⁡ ( | ϕ ϕ ⟩ ⟩ ⟨ ⟨ ϕ ϕ | ) , and likewise for p B , represent the reduced density matrices for either particle. The following protocol is then used: