Traditionally, medical imaging techniques such as PET (positron emission tomography) and SPECT (single-photon emission computed tomography) have relied on mechanical collimators to detect the sources of photons. This limits the image's resolution and field of view. To improve upon this, Compton cameras have emerged as a promising alternative. The principle is to measure the angle of a photon scattered in the detector, which indicates the likely sources in the form of a cone culminating in the position of the interaction. The cones from multiple events may be superimposed in order to generate an image. The object of this work is to use list-mode likelihood methods to better reconstruct the source image from the data recorded by a simulated Compton camera in the case of a solid detector volume with good spatial- and energy resolution.  The results demonstrate an improvement of image quality for reconstructions of single point source and multiple extended sources. In addition, the results indicate that our used algorithm converges for point sources. The minimum number of measured events for accurate reconstruction for different source distributions remains to be determined, and the algorithm's ability to resolve closely adjacent sources should be investigated more.