Abstract: Objective. To demonstrate the benefits of using an joint image reconstruction algorithm based on the List Mode Maximum Likelihood Expectation Maximization that combines events measured in different channels of information of a Compton camera. Approach. Both simulations and experimental data are employed to show the algorithm performance. Main results. The obtained joint images present improved image quality and yield better estimates of displacements of high-energy gamma-ray emitting sources. The algorithm also provides images that are more stable than any individual channel against the noisy convergence that characterizes Maximum Likelihood based algorithms. Significance. The joint reconstruction algorithm can improve the quality and robustness of Compton camera images. It also has high versatility, as it can be easily adapted to any Compton camera geometry. It is thus expected to represent an important step in the optimization of Compton camera imaging.