  A knot type is exchange reducible if an arbitrary closed n-braid
representative can be changed to a closed braid of minimum braid index by a
finite sequence of braid isotopies, exchange moves and +/- destabilizations. In
the manuscript [J Birman and NC Wrinkle, On transversally simple knots,
preprint (1999)] a transversal knot in the standard contact structure for S^3
is defined to be transversally simple if it is characterized up to transversal
isotopy by its topological knot type and its self-linking number. Theorem 2 of
Birman and Wrinkle [op cit] establishes that exchange reducibility implies
transversally simplicity. The main result in this note, establishes that
iterated torus knots are exchange reducible. It then follows as a Corollary
that iterated torus knots are transversally simple.
