  We consider superstring theory on AdS_3 x S^3 x T^4 supported by a
combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q).
This theory interpolates between the pure RR flux model (q=0) whose spectrum is
expected to be described by a Bethe ansatz and the pure NSNS flux model (q=1)
which is described by the supersymmetric extension of the SL(2,R) x SU(2) WZW
model. As a first step towards the solution of this integrable theory for
generic value of q we compute the corresponding tree-level S-matrix for massive
BMN-type excitations. We find that this S-matrix has a surprisingly simple
dependence on q: the diagonal amplitudes have exactly the same structure as in
the q=0 case but with the BMN dispersion relation e^2 = p^2 + 1 replaced by the
one with shifted momentum and mass, e^2 = (p + q)^2 + 1 - q^2. The off-diagonal
amplitudes are then determined from the classical Yang-Baxter equation. We also
construct the Pohlmeyer reduced model corresponding to this superstring theory
and find that it depends on q only through its mass-squared parameter
proportional to (1-q^2), implying that its relativistic S-matrix is
q-independent.
