New methods for inverting Compton camera data have recently been developed. In particular, an inversion method was developed for each of the two models of Compton camera data that have been proposed in the literature. These methods make it possible to produce a parallel projection as well as a "voxel-wise" reconstruction of a distribution of radioactivity. An objective of the computer simulations presented here is to demonstrate these methods' ability to produce parallel projections and voxel-wise reconstructions. The results of the simulations indicate the new inversion methods can produce reasonable images and projections, at least when noiseless simulated data is used. Furthermore, the minimum sets of data needed to use these inversion methods were also recently determined. Presumably, incorporating more measurements into the reconstruction process than the minimum needed will improve the quality of the reconstructions that result. Methods for doing this are developed here as well.