To determine the potential of spectral computed tomography (CT) with Medipix3 for quantifying fat, calcium, and iron in soft tissues within small animal models and surgical specimens of diseases such as fatty liver (metabolic syndrome) and unstable atherosclerosis. The spectroscopic method was applied to tomographic data acquired using a micro-CT system incorporating a Medipix3 detector array with silicon sensor layer and microfocus x-ray tube operating at 50 kVp. A 10 mm diameter perspex phantom containing a fat surrogate (sunflower oil) and aqueous solutions of ferric nitrate, calcium chloride, and iodine was imaged with multiple energy bins. The authors used the spectroscopic characteristics of the CT number to establish a basis for the decomposition of soft tissue components. The potential of the method of constrained least squares for quantifying different sets of materials was evaluated in terms of information entropy and degrees of freedom, with and without the use of a volume conservation constraint. The measurement performance was evaluated quantitatively using atheroma and mouse equivalent phantoms. Finally the decomposition method was assessed qualitatively using a euthanized mouse and an excised human atherosclerotic plaque. Spectral CT measurements of a phantom containing tissue surrogates confirmed the ability to distinguish these materials by the spectroscopic characteristics of their CT number. The assessment of performance potential in terms of information entropy and degrees of freedom indicated that certain sets of up to three materials could be decomposed by the method of constrained least squares. However, there was insufficient information within the data set to distinguish calcium from iron within soft tissues. The quantification of calcium concentration and fat mass fraction within atheroma and mouse equivalent phantoms by spectral CT correlated well with the nominal values (R(2) = 0.990 and R(2) = 0.985, respectively). In the euthanized mouse and excised human atherosclerotic plaque, regions of calcium and fat were appropriately decomposed according to their spectroscopic characteristics. Spectral CT, using the Medipix3 detector and silicon sensor layer, can quantify certain sets of up to three materials using the proposed method of constrained least squares. The system has some ability to independently distinguish calcium, fat, and water, and these have been quantified within phantom equivalents of fatty liver and atheroma. In this configuration, spectral CT cannot distinguish iron from calcium within soft tissues.