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In order to improve the security by providing the stego image with imperceptible quality, three different steganographic methods for gray level images are presented in this paper. Four Neighbors, diagonal neighbors and eight neighbors methods are employed in our scheme. These methods utilize a pixel's dependency on its neighborhood and psycho visual redundancy to ascertain the smooth areas and edged areas in the image. In smooth areas we embed three bits of secret information. In the edged areas, variable rate bits are embedded. From the experimental results it is seen that the proposed methods achieve a much higher visual quality as indicated by the high peak signal-to-noise ratio (PSNR) in spite of hiding a larger number of secret bits in the image. In addition, to embed this large amount of secret information, at most only half of the total number of pixels in an image is used. Moreover, extraction of the secret information is independent of original cover image.