The simple problem presented in this paper will allow me to more thoroughly understand CIPR. One issue I plan to examine is its effect on amplitudes. An extension of this issue is the possibility of using the model normalization described by Rickett (2001a,b) to normalize the result of the preconditioned iterations before it is sent to the regularized inversion as an initial model. Another issue is the possibility of applying a mask that will only allow the preconditioning and regularization to occur within a specified area. Also, I plan to find some way to determine the optimal ratio of preconditioned iterations to regularized iterations. This may be related to another concern I intend to scrutinize, which is the effect of CIPR on the final residuals.