  We study the scattering of magnon boundstates in the spin-chain description
of planar N=4 SUSY Yang-Mills. Starting from the conjectured exact S-matrix for
magnons in the SU(2) sector, we calculate the corresponding S-matrix for
boundstates with an arbitrary number of constituent magnons. The resulting
expression has an interesting analytic structure with both simple and double
poles. We also calculate the semiclassical S-matrix for the scattering of the
corresponding excitations on the string worldsheet known as Dyonic Giant
Magnons. We find precise agreement with the magnon boundstate S-matrix in the
limit of large 't Hooft coupling.
