  We bootstrap the all-loop dynamic S-matrix for the homogeneous psu(1,1|2)^2
spin-chain believed to correspond to the discretization of the massive modes of
string theory on AdS_3 x S^3 x T^4. The S-matrix is the tensor product of two
copies of the su(1|1)^2 invariant S-matrix constructed recently for the
d(2,1;alpha)^2 chain, and depends on two antisymmetric dressing phases. We
write down the crossing equations that these phases have to satisfy.
Furthermore, we present the corresponding Bethe Ansatz, which differs from the
one previously conjectured, and discuss how our construction matches several
recent perturbative calculations.
