  The maximum entanglement between two coupled qubits in the steady state under
two independent incoherent sources of excitation is reported. Asymmetric
configurations where one qubit is excited while the other one dissipates the
excitation are optimal for entanglement, reaching values three times larger
than with thermal sources. The reason is the purification of the steady state
mixture (that includes a Bell state) thanks to the saturation of the pumped
qubit. Photon antibunching between the cross emission of the qubits can be used
to experimentally evidence the large degrees of entanglement.
