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In image steganography, a pixel can carry secret bits by choosing adding/subtracting one to/from the gray value. This kind of"±1 steganography" can hide a longer message than simple LSB embedding. We propose a double-layered embedding method for implementing "±1 steganography," in which binary covering codes and wet paper codes are used to hide messages in the LSB plane and the second LSB plane, respectively. We show that this method can achieve the upper bound on the embedding efficiency of"±1 steganography" when the employed binary covering codes reach the upper bound on that of LSB steganography. Applications using random and structured covering codes show that the new method outperforms previous ones and can approach the upper bound. [ABSTRACT FROM AUTHOR]