  String theory on AdS_3 x S^3 x T^4 geometries supported by a combination of
NS-NS and R-R charges is believed to be integrable. We elucidate the kinematics
and analytic structure of worldsheet excitations in mixed charge and pure NS-NS
backgrounds, when expressed in momentum, Zhukovsky variables and the rapidity
$u$ which appears in the quantum spectral curve. We discuss the relations
between fundamental and bound state excitations and the role of fusion in
constraining and determining the S matrices of these theories. We propose a
scalar dressing factor consistent with a novel $u$-plane periodicity and
comment on its close relation to the XXZ model at roots of unity. We solve the
odd part of crossing and show that our solution is consistent with fusion and
reduces in the relativistic limit to dressing phases previously found in the
literature.
