  A wide range of applications, most notably in comparative genomics, involve
the computation of a shortest sorting sequence of operations for a given
permutation, where the set of allowed operations is fixed beforehand. Such
sequences are useful for instance when reconstructing potential scenarios of
evolution between species, or when trying to assess their similarity. We
revisit those problems by adding a new constraint on the sequences to be
computed: they must \emph{avoid} a given set of \emph{forbidden intermediates},
which correspond to species that cannot exist because the mutations that would
be involved in their creation are lethal. We initiate this study by focusing on
the case where the only mutations that can occur are exchanges of any two
elements in the permutations, and give a polynomial time algorithm for solving
that problem when the permutation to sort is an involution.
