This paper explores the statistics of least-significant bit (LSB) steganography. The problem of encoding a bit sequence (message) to match the statistics of a random bit-sequence (cover) is considered. A method of hiding information in the least significant bits (LSBs) of JPEG coefficients is described; the method mimics either the chi-square statistic of JPEG coefficients or their distribution. The method uses two-bit codes to encode the message bits. It is shown to be very effective on JPEG images of natural scenes.