In this paper, we have proposed an extended version of Absolute Moment Block Truncation Coding (AMBTC) to compress images. Generally the elements of a bitplane used in the variants of Block Truncation Coding (BTC) are of size 1 bit. But it has been extended to two bits in the proposed method. Number of statistical moments preserved to reconstruct the compressed has also been raised from 2 to 4. Hence, the quality of the reconstructed images has been improved significantly from 33.62 to 38.12 with the increase in bpp by 1. The increased bpp (3) is further reduced to 1.75in multiple levels: in one level, by dropping 4 elements of the bitplane in such a away that the pixel values of the dropped elements can easily be interpolated with out much of loss in the quality, in level two, eight elements are dropped and reconstructed later and in level three, the size of the statistical moments is reduced. The experiments were carried over standard images of varying intensities. In all the cases, the proposed method outperforms the existing AMBTC technique in terms of both PSNR and bpp.