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A detailed examination of the original calibration data for the laboratory version of the Mars Exploration Rover alpha particle X-ray spectrometer is undertaken to ascertain if the results from a suite of certified geochemical reference materials (GRMs) agree with the APXS calibration based upon homogeneous standards which was established in the previous paper. Various discrepancies, some of them large, are observed for specific elements in specific rock types, and it is argued on the basis of X-ray diffraction analyses of the GRMS that these are caused by the mineral phase structure of the rocks. Elements present in accessory mineral phases can be subject to very large errors, necessitating caution in interpretation of trace element results from the APXS. Some of the discrepancies can be dealt with by developing sub-calibrations, each of which is “tuned” to a specific rock type. This approach has the potential to provide more accurate APXS analysis of unknown rocks than a calibration scheme based upon a simple averaging over many rock types within a GRM suite, or over a mix of rock and homogeneous standards. It also has the potential to measure the content of mineralogically bound water provided that a means of determining the distance from sample to detector is available.