  Type II supergravity admits an AdS(3) x S(2) x S(2) x T(3) solution with
fluxes depending on several free parameters. We determine the constraints on
these parameters imposed by the requirement of (classical) integrability of the
superstring sigma model. To do this we analyze the low-energy effective action
for the spinning GKP string. The absence of particle production in the
tree-level S-matrix of bosonic excitations is shown to imply the vanishing of
two of the four parameters in the NSNS three-form flux. This reduces the
supergravity background to either the one-parameter AdS(3) x S(2) x S(2) x T(3)
background preserving eight supersymmetries, or a non-supersymmetric branch,
which differs only by flipping a sign in the RR flux. We show that both these
branches can be obtained from AdS(3) x S(3) x S(3) x S(1) by T-dualities on the
(Hopf) circle fibers of the three-spheres and therefore the integrability of
the string in these backgrounds follows.
