In this paper, we perform a statistical analysis of curvelet coefficients, distinguishing between two classes of coefficients: those that contain a significant noise-free component, which we call "signal of interest", and those that do not. By investigating the marginal statistics, we develop a prior model for curvelet coefficients. The analysis of the joint intra- and inter-band statistics enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we present a novel denoising method, inspired by a recent wavelet domain method ProbShrink. The new method outperforms its wavelet-based counterpart and produces results that are close to those of state-of-the-art denoisers.