Information from the many kinds of spectroscopy used by chemists and physicists is fundamental to our understanding of the structure of materials. Numerical techniques have an important role to play in the augmentation of the instrumentation and technology available in the laboratory, but are frequently viewed as separate from the laboratory procedures. We examine the model approaches which are currently applied in spectroscopy and determine their applicability to piezo-spectroscopic data. Typically, in piezo-spectroscopic modelling the analyses in question are required to handle large complex secular matrices, to distinguish between components in the experimental results, and to identify the transition types as rapidly and as efficiently as possible. The method proposed is based on providing a shell to the Powell or Fletcher-Reeves minimisation algorithms, and gives favourable results compared to those previously used. Additionally, the statistical properties of the least-squares estimator used in the Powell-shell are examined and implications for nonlinear model functions are discussed. We also show that the least squares estimator performs well for piezo-spectroscopic data compared to those currently used in multi-response data analysis. Finally we describe the development of a software tool which incorporates all features of fitting piezo-spectroscopic data.