ABT is the reference algorithm for asynchronous distributed constraint satisfaction. When searching, ABT produces nogoods as justifications of deleted values. When one of such nogoods has an empty left-hand side, the considered value is eliminated unconditionally, once and for all. This value deletion can be propagated using standard arc consistency techniques, producing new deletions in the domains of other variables. This causes substantial reductions in the search effort required to solve a class of problems. We also extend this idea to the propagation of conditional deletions, something already proposed in the past. We provide experimental results that show the benefits of the proposed approach, especially considering communication cost.