We show that a family of tree languages W_{(l,k)}, previously used by J. Bradfield, and by the first author to show the strictness of the Rabin¨CMostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. theWadge reducibility. That is, W_{(l,k) ⩽_W W_{(l',k')} if and only if the index (l', k') is above (l, k). This is one of the few separation results known so far, concerning the topological complexity of non-deterministically recognizable tree languages, and one of the few results about finite-state recognizable non-Borel sets of trees.
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