Impact-source X-ray microtomography (XMT) is a widely-used benchtop alternative to synchrotron radiation microtomography. Since X-rays from a tube are polychromatic, however, greyscale ‘beam hardening' artefacts are produced by the preferential absorption of low-energy photons in the beam path. A multi-material ‘carousel' test piece was developed to offer a wider range of X-ray attenuations from well-characterised filters than single-material step wedges can produce practically, and optimization software was developed to produce a beam hardening correction by use of the Nelder-Mead optimization method, tuned for specimens composed of other materials (such as hydroxyapatite [HA] or barium for dental applications.) The carousel test piece produced calibration polynomials reliably and with a significantly smaller discrepancy between the calculated and measured attenuations than the calibration step wedge previously in use. An immersion tank was constructed and used to simplify multi-material samples in order to negate the beam hardening effect of low atomic number materials within the specimen when measuring mineral concentration of higher-Z regions. When scanned in water at an acceleration voltage of 90 kV a Scanco AG hydroxyapatite / poly(methyl methacrylate) calibration phantom closely approximates a single-material system, producing accurate hydroxyapatite concentration measurements. This system can then be corrected for beam hardening for the material of interest.