The application of calibration and prediction (CAP) to joint measurements of near-infrared (NIR) and Raman spectra for the same reference data requires the development of joint inversion methodologies for the implementation of the calibration step. Joint inversion has been successfully utilized in geophysical prospecting and in medical diagnosis, where the need to perform CAP is not involved. However, the obvious ways in which joint inversion might be implemented in spectroscopy, where some form of CAP must be performed, do not appear to work. Here, a new methodology, leap-frog calibration and prediction (LF-CAP), is proposed. It allows naturally for the information in the joint NIR and Raman spectra to yield a quite robust predictor of the property of interest. This new procedure is examined in some detail. The major limitation of CAP, as a strategy for recovering information from indirect measurements, is that it is a one-step process, in that the calibration step can only be applied once. If multiple independent spectral data are available for the same reference data, then the leap-frog implementation of CAP turns the recovery of information into an iterative process that converges under a wide range of circumstances.