  We investigate efficient entanglement purification through double selection
process. This method works with higher noise thresholds for the communication
channels and local operations, and achieves higher fidelity of purified states.
Furthermore it provides a yield comparable to the usual protocol with single
selection. It is shown by general considerations that the double selection is
optimal to remove the first-order errors, achieving the upper bound on the
fidelity of purified states in the low noise regime. The double selection is
also applied to purification of multi-partite entanglement such as
two-colorable graph states.
