In this paper we propose new filters for the contourlet transform and derive a series of trigonometric filters. Furthermore, we propose a methodology for designing new filters that are obtained from polynomial functions. Thus, we jointly derive different filters for each contourlet decomposition level, and apply them in image denoising. We show that on all the tested images and noise levels, the contourlet transform equipped with the proposed filters clearly outperforms its raised cosine filter-based counterpart in terms of denoising performance. In this sense, when employing polynomial filters, we report gains of up to 0.6dB.