Motivated by the ongoing investigation of SrCu2(BO3)(2) under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/2 model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective S = 1 Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.