This paper deals with the implementation of a new compression methodology, which uses curvelet coefficients with SPIHT (Set Partitioning In Hierarchical Trees) encoding scheme. The first phase deals with the transformation of the stimulus image into the curvelet coefficients. The curvelet transform is a new family of multi-scale representation containing the information about the scale and location parameters. Unlike wavelets, it also contains the directional parameters. The orientation selectivity behavior and anisotropic nature of the curvelet transform helps to represent suitably the objects with curves and handles other two-dimensional singularities better than wavelets, which makes it a more proficient transformation for image compression application. During the second phase, a threshold-based selection mechanism has been developed to get prominent coefficients out of different scales. Final phase deals with the application of lossy SPIHT encoding technique on selected significant coefficients. SPIHT exploits the multi-scale nature of curvelet transform and removes the statistical and subjective redundancies. The empirical results on standard test images provide higher PSNR than some of the previous approaches, which strengthen the idea of using curvelet transform instead of wavelet transform in order to get lesser bits to represent more prominent features. Keywords: Curvelet Coefficients, SPIHT, Multi-resolution Analysis