A new least-significant-bit (LSB)-based steganographic model providing high capacity is proposed. This model is based on the idea of statistical minimum mean square error (MSE) replacement and can be implemented in two schemes: the oblivious scheme and the cover escrow scheme. In both schemes, blockwise replacement is adopted in the hiding process based on the statistical characteristics of a cover image and a hidden image. Two operations, mean shifting and phase reversing, are used to modulate the subblocks of both the hidden and cover images, which contributes to minimizing the MSE introduced by LSB-based replacement. Examples are shown to demonstrate their effectiveness. Performance analysis is also done to provide the upper limits of the improvement by the two schemes in the ideal cases. Finally, experimental results with real images are presented to demonstrate the effectiveness of the proposed model.