The simple experiment conducted in this paper has compared two familiar inversion schemes, preconditioned and regularized, with a new combined inversion scheme that uses the result of a small number of preconditioned iterations as an initial model for a small number of regularized iterations (CIPR). I used a simple interpolation problem to test CIPR's ability to reduce the number of iterations needed to get an ``improved'' model. This ``improved'' model has a solution defined at every point and has a frequency content close to that of an ``ideal'' model. I have shown that to obtain an ``improved'' model, CIPR takes far fewer iterations than either of the other schemes. This makes CIPR an interesting option for many types of seismic inversion problems.