  We obtain the all-loop worldsheet S matrix for fundamental excitations on
AdS_3 x S^3 x T^4 by studying the off-shell symmetry algebra of the superspace
action in lightcone gauge. The massless modes, unaccounted for in earlier
works, are automatically included in our treatment. Their exact dispersion
relation is found to be non-relativistic, of giant-magnon form and their
scattering is naturally well-defined. This opens the way to a complete
investigation of AdS_3/CFT_2 integrability.
