TWo entropy coding schemes are investigated in this paper by estimating the entropies that specify the lower bounds of their coding rates. In the firSt scheme, we use a traditional combination of runlength and Huffman codes. Arithmetic codes are used in the second scheme. The results indicate that binary arithmetic codes outperform runlength codes by a factor of 34 % for low-rate coding of the zero-valued coefficients of the cosine transform of digital images. Hexadecimal truncated arithmetic codes provided a coding rate improvement as high as 28 % over truncated Huffman codes at low rates. The complexity of these arithmetic codes is suitable for practical implementation.