Purpose: Polyenergetic Alternating Minimization (AM) is a statistical image reconstruction (SIR) algorithm that uses a precomputed estimated x‐ray spectrum to directly model beam hardening effects in the course of iteratively reconstructing CT images. We hypothesize that SIR reconstructions, based upon a rigorous physical model of the CT signal formation process, are of better quality than filtered‐backprojection images using conventional preprocessing beam‐hardening corrections. This presentation focuses on the accuracy and magnitude of artifacts in polyenergetic Alternating Minimization (AM) images of homogeneous phantoms. Method and Materials: The x‐ray spectrum of a Brilliance CT scanner was estimated from transmission measurements through varying thicknesses of aluminum and polymethyl methacrylate (PMMA) filters. An exhaustive search was used to find the semi‐empirical Birch‐Marshall x‐ray spectrum that most closely reproduced the transmission measurements. The polyenergetic AM algorithm was used to reconstruct images of 4 homogeneous PMMA disks of varying diameters using the estimated spectrum and measured scatter corrections. A simple test of the algorithm is performed: reconstructing PMMA disks using a PMMA basis in the AM algorithm should reconstruct an image intensity of 1.0 for all disk diameters. Mean intensity and noise are evaluated for disk center and periphery. Results: Our estimated spectrum fits the PMMA transmission measurements to within 1.5%. The AM algorithm reconstructs uniform images of the PMMA disks with mean intensity within 0.8% of the expected relative PMMA density for all disk sizes and locations. Relative standard deviations of the reconstructed intensities about the mean vary between 1.9% and 0.6% (center and periphery) for the 30 cm disk and 0.15% and 0.14% for the 5 cm disk. Conclusion: The polyenergetic AM algorithm can reconstruct accurate images from experimentally acquired CT data. However, great care must be taken in the processing of the raw CT data and the x‐ray spectrum estimation.