  We investigate the physically allowed probabilities for transforming one
N-partite W-class state to another by means of local operations assisted with
classical communication (LOCC). Recently, Kintas and Turgut have obtained an
upper bound for the maximum probability of transforming two such states
[arXiv:1003.2118v1]. Here, we provide a simple sufficient and necessary
condition for when this upper bound can be satisfied and thus when optimality
of state transformation can be achieved. Our discussion involves obtaining
lower bounds for the transformation of arbitrary W-class states and showing
precisely when this bound saturates the bound of [arXiv:1003.2118v1]. Finally,
we consider the question of transforming symmetric W-class states and find that
in general, the optimal one-shot procedure for converting two symmetric states
requires a non-symmetric filter by all the parties.
