  Starting from the integrable two-loop spin-chain Hamiltonian describing the
anomalous dimensions of scalar operators in the planar N=6 superconformal
Chern-Simons theory of ABJM, we perform a direct coordinate Bethe ansatz
computation of the corresponding two-loop S-matrix. The result matches with the
weak-coupling limit of the scalar sector of the all-loop S-matrix which we have
recently proposed. In particular, we confirm that the scattering of A and B
particles is reflectionless. As a warm up, we first review the analogous
computation of the one-loop S-matrix from the one-loop dilatation operator for
the scalar sector of planar N=4 superconformal Yang-Mills theory, and compare
the result with the all-loop SU(2|2)^{2} S-matrix.
