Spectral X-ray imaging allows to differentiate between two given tissue types, provided their spectral absorption characteristics differ measurably. In mammography, this method is used clinically to determine a decomposition of the breast into adipose and glandular tissue compartments, from which the glandular tissue fraction and, hence, the volumetric breast density (VBD) can be computed. Another potential application of this technique is the characterization of lesions by spectral mammography. In particular, round lesions are relatively easily detected by experienced radiologists, but are often difficult to characterize. Here, a method is described that aims at discriminating cystic from solid lesions directly on a spectral mammogram, obtained with a calibrated spectral mammography system and using a hypothesis-testing algorithm based on a maximum likelihood approach. The method includes a parametric model describing the lesion shape, compression height variations and breast composition. With the maximum likelihood algorithm, the model parameters are estimated separately under the cyst and solid hypothesis. The resulting ratio of the maximum likelihood values is used for the final tissue characterization. Initial results using simulations and phantom measurements are presented.