A new compression algorithm for fingerprint images is introduced. A modified wavelet packet scheme which uses a fixed decomposition structure, matched to the statistics of fingerprint images, is used. Based on statistical studies of the subbands, different compression techniques are chosen for different subbands. The decision is based on the effect of each subband on reconstructed image, taking into account the characteristics of the Human Visual System (HVS). A noise shaping bit allocation procedure which considers the HVS, is then used to assign the bit rate among subbands. Using Lattice Vector Quantization (LVQ), a new technique for determining the largest radius of the Lattice and its scaling factor is presented. The design is based on obtaining the smallest possible Expected Total Distortion (ETD) measure, using the given bit budget. At low bit rates, for the coefficients with high-frequency content, we propose the Positive-Negative Mean (PNM) algorithm to improve the resolution of the reconstructed image. Furthermore, for the coefficients with low-frequency content, a lossless predictive compression scheme is developed. The proposed algorithm results in a high compression ratio and a high reconstructed image quality with a low computational load compared to other available algorithms.