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Steganography is an ancient art of conveying messages in a secret way that only the receiver knows the existence of a message. So a fundamental requirement for a steganographic method is imperceptibility; this means that the embedded messages should not be discernible to the human eye. There are two other requirements, one is to maximise the embedding capacity, and the other is security. The least-significant bit (LSB) insertion method is the most common and easiest method for embedding messages in an image. However, how to decide on the maximal embedding capacity for each pixel is still an open issue. An image steganographic model is proposed that is based on variable-size LSB insertion to maximise the embedding capacity while maintaining image fidelity. For each pixel of a grey-scale image, at least four bits can be used for message embedding. Three components are provided to achieve the goal. First, according to contrast and luminance characteristics, the capacity evaluation is provided to estimate the maximum embedding capacity of each pixel. Then the minimum-error replacement method is adapted to find a grey scale as close to the original one as possible. Finally, the improved grey-scale compensation, which takes advantage of the peculiarities of the human visual system, is used to eliminate the false contouring effect. Two methods, pixelwise and bitwise, are provided to deal with the security issue when using the proposed model. Experimental results show effectiveness and efficiency of the proposed model.