It is shown how the performances of SAW gas sensors can be optimized based on pure acoustic peculiarities of SAW propagation in anisotropic single crystals. For a given gas and sensitive membrane, the calibration curve (dependence of the response R versus gas concentration n), the sensitivity S (slope of the calibration curve: S = dR/dn), the detection limit nth, (cut-off of the curve at the threshold Pthr), and the resolution deltan of the sensor (recognition of two close concentrations) can be controlled by a proper choice of the substrate material and its crystallographic orientation (cut and direction of the SAW propagation). An experimental test of this property is performed on SAW devices implemented on different substrate materials and crystallographic orientations, both uncoated or coated, with a sorbent membrane of polycrystalline Pd or Pd:Ni film, upon exposure to humid air as a test analyte.