The performance of digital subscriber line (DSL) systems, such as ADSL and VDSL is limited by crosstalk. Suppression of in-domain far-end self crosstalk using vectoring technology enables very high bidirectional data rates over twisted-pairs of copper wires. However, the performance of vectored DSL systems is severely degraded in the presence of alien or out-of-domain crosstalk that arises from sources that lie outside the vectored DSL system and share the same cable binder. In this paper, we propose a practical, non-iterative, high performance algorithm for alien crosstalk mitigation. Simulation results and complexity analysis corresponding to a vectored VDSL2 system in presence of alien crosstalk are presented to illustrate the significant performance gains of the proposed algorithm and its low implementation complexity.