The remote determination of dielectric constants of stratified dielectrics, through solution of the inverse-scattering problem, has practical application in many fields. We use a simple one-dimensional model to determine the salient characteristics of stratified layers of dielectrics given a finite number of reflection coefficients for various frequencies in the microwave X-band region. One of the key concepts of this research is the optimization that is necessary to find a global minimum of the highly nonlinear function that specifies the scattering coefficients