Recent work in CT image reconstruction has seen increasing interest in the use of compressive sensing (CS) techniques to reconstruct images from sparse-view projection data. The underlying principle of CS is that if an image is known to be sparse (or, more typically, the result of some transform applied to the image is sparse), then the image can be accurately reconstructed from fewer samples than are required without the sparsity assumption. To date, most work in this area has used a linear model for acquisition of CT data, which implicitly assumes that the x-ray beam used to generate the data is monoenergetic. Most x-ray beams used in clinical systems are polyenergetic, however, which is inconsistent with this linear model. This inconsistency produces so-called beam hardening artifacts. In this talk I will present a novel reconstruction algorithm that combines techniques for reconstruction of polyenergetic CT data with ideas from compressive sensing. The algorithm is able to produce images from undersampled projection data that are largely free of beam hardening artifacts.