Large volumes of fingerprints are collected and stored every day in a wide range of applications, including forensics, access control etc., and are evident from the database of Federal Bureau of Investigation (FBI) which contains more than 70 million finger prints. Wavelet based Algorithms for image compression are the most successful, which result in high compression ratios compared to other compression techniques. Even though wavelet bases are providing good compression ratios, they are not optimal for representing images consisting of different regions of smoothly varying grey-values, separated by smooth boundaries. This issue is addressed by the directional transforms, known as contourlets which have the property of preserving edges. This paper focuses mainly on the new fingerprint compression using contourlet transform (CT), which includes elaborated repositioning algorithm for the CT coefficients, and Modified set partitioning in hierarchical trees (SPIHT) which is applied to get better quality, i.e., high peak signal to noise ratio (PSNR). The results obtained are tabulated and compared with those of the wavelet based ones.