Standard JPEG decompression reconstructs quantized DCT coefficients to the center of the quantization bin. This fails to exploit the nonuniform distribution of the AC coefficients. Assuming a Laplacian distribution, we derive a maximum likelihood estimate of the Laplacian parameter, based on the quantized coefficients available at the decoder, and use this estimate to optimally bias the reconstruction levels during decompression. As a decoder enhancement, this technique is fully compatible with the JPEG standard and does not modify the JPEG compressed bit stream. Extensive simulations indicate that, at typical compression ratios, biased re-construction results in modest PSNR improvements - about 0.25 dB or higher - and slight subjective improvements, for little or no computational cost. Furthermore, simulations show that the PSNR improvements are very close (within 0.07 dB) to the best theoretically possible.