The conventional method for sending halftone images via facsimile machines is inefficient. The ToneFac algorithm previously proposed improves the efficiency of halftone image transmission. ToneFac represents a halftone image by mean block values and an error image. To improve on ToneFac, this paper proposes 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.