The conventional method for sending halftone images via facsimile machines is inefficient. The previously proposed ToneFac algorithm improves the transmission of halftone images. ToneFac represents a halftone image by mean gray values of the disjoint blocks and an error image, which records the difference between the desired halftone and the halftone generated using the mean gray values. To improve on ToneFac, we propose additional processing techniques: searching for the error-minimizing gray value for each block; quantization and coding of block values; bit switching, which transforms the error image into a more compressible image; optimal block sizing; and spurious dot filtering, which removes perceptually insignificant dots. The new algorithm is compared to other methods, including adaptive arithmetic coding, and is shown to provide improvement in bit rate. A theoretical consideration of the compression ratio from the ToneFac algorithm is also given.