The technique of cepstrum thresholding, which is shown to be an effective, yet simple, way of obtaining a smoothed non parametric spectrum estimate of a stationary signal. The major problem of this method is the choice of the threshold value for variance reduction of spectrum estimates. This paper proposes a new threshold selection method which is based on cross validation schemes such as Leave-One-Out, LeaveTwo-Out and Leave-Half-Out. This new methods are easy to describe, simple to implement, and does not impose severe conditions on the unknown spectrum. Numerical results suggest that this new methods are shown to be in agreement with those obtained when the spectrum is fully known.