  We introduce a class of sets of words which is a natural common
generalization of Sturmian sets and of interval exchange sets. This class of
sets consists of the uniformly recurrent tree sets, where the tree sets are
defined by a condition on the possible extensions of bispecial factors. We
prove that this class is closed under maximal bifix decoding. The proof uses
the fact that the class is also closed under decoding with respect to return
words.
