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. Models of the response of the specimen to at least two different measurement technologies share at least one common geometric parameter. In some embodiments, a model building and analysis engine performs x-ray and optical analyses wherein at least one common parameter is coupled during the analysis. The fitting of the response models to measured data can be done sequentially, in parallel, or by a combination of sequential and parallel analyses. 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. For example, a geometric model of the specimen is restructured based on the fit between the response models and corresponding measurement data.