Structural parameters of a specimen are determined by fitting models of the response of the specimen to measurements collected by different measurement techniques in a combined analysis. X-ray measurement data of a specimen is analyzed to determine at least one specimen parameter value that is treated as a constant in a combined analysis of both optical measurements and x-ray measurements of the specimen. For example, a particular structural property or a particular material property, such as an elemental composition of the specimen, is determined based on x-ray measurement data. The parameter(s) determined from the x-ray measurement data are treated as constants in a subsequent, combined analysis of both optical measurements and x-ray measurements of the specimen. In a further aspect, the structure of the response models is altered based on the quality of the fit between the models and the corresponding measurement data.