<p>We present two entanglement concentration protocols (ECPs) for unknown less-entangled states. Different from conventional ECPs where two or more copies of less-entangled states are selected from the same ensemble, here we describe two general ECPs for two initially nonidentical less-entangled states. In the first protocol, we suppose the coefficients of the two initial entangled states are different. While in the second protocol, we suppose not only the coefficients but also the bit information are different between the two initial entangled states. We show that the successful operation of a conventional ECP may not obtain a more entangled state, while the discarded source pair, which is usually regarded as a failure in conventional ECPs, may have more entanglement than the initial one. We give the criteria of the successful concentration to obtain a more entangled state. Our ECPs may have potential application in practical long-distance quantum communications.</p>