The concept of a model operator as a preconditioner is one of the widely used for the solution of large elliptic grid systems. During the last decade it gained a recognition in some ``nonelliptic'' applications like the solution of systems with Toeplitz matrix \(A\) which arise, for example, in signal processing and control theory. The authors present a very interesting theory dealing with circulant preconditioners \(C=C^*>0\). They suggest to obtain the known cases of \(C\) on the base of several convolutions of the generating function of \(A\) with specified kernels. The case of the Dirac delta function leads to a new \(C\). All constructions give spectra of \(C^{-1}A\) clustered around 1, thus, the rapid convergence of the modified (preconditioned) conjugate gradient method is predicted.