Proximal point algorithms are applicable to a variety of settings in optimization. See Rockafellar, R.T. (1976), and Spingarn, J.E. (1981) for examples. We consider a simple idealized proximal point algorithm using gradient minimization on C2convex functions. This is compared to the direct use of the same gradient method with an appropriate mollifier. The comparison is made by determining estimates of the costrequired to reduce the function to a given precision E. Our object is to assess the potential efficiency of these algorithms even if we do not know how to realize this potential.