We discuss the problem of determining the minimum reflectance achievable with a given inhomogeneous layer thickness, substrate input impedance and range of allowed material parameters for normally incident, monochromatic sound waves. The density and dilitation modulus are permitted to vary independently. Real and complex moduli are considered. In the case of real parameters, analytic solutions for the switching curves and sublayer thicknesses of the multilayer system are presented. The resulting sublayer sequences will be discussed. The sequences are periodic and we show that for certain combinations of parameters the reduced unit cell thickness is approximately equal to 2π radians. General results concerning the parametrization of sublayers in the case of complex moduli will be discussed. Examples of particular solutions will be presented.