This paper proposes a new cepstrum estimation procedure that is capable of producing smoother and improved cepstrum estimates without the use of any parametric modeling. This procedure consists of two main steps: In the first step, it applies a so-called grid transformation to the empirical cepstral coefficients, while in the second step it nonparametrically smooths the transformed coefficients with local linear regression. The Stein's unbiased risk estimation (SURE) approach is adopted to select both the extent of the grid transformation and the amount of smoothing. It is shown that the use of this SURE selection method for the current problem is asymptotically optimal in a well-defined sense. Lastly, the good practical performance of the new cepstrum estimation procedure is demonstrated via numerical experiments.