In this article we examine a scheme that uses two alternating Huffman codes to encode a discrete independent and identically distributed source with a dominant symbol. One Huffman code encodes the length of runs of the dominant symbol, the other encodes the remaining symbols. We call this combined strategy alternating runlength Huffman (ARH) coding. This is a popular scheme, used for example in the efficient pyramid image coder (EPIC) subband coding algorithm. Since the runlengths of the dominant symbol are geometrically distributed, they can be encoded using the Huffman codes identified by Golomb (1966) and later generalized by Gallager and Van Voorhis (1975). This runlength encoding allows the most likely symbol to be encoded using less than one bit per sample, providing a simple method for overcoming a drawback of prefix codes-that the redundancy approaches one as the largest symbol probability P approaches one. For ARH coding, the redundancy approaches zero as P approaches one. Comparing the average code rate of ARH with direct Huffman coding we find that: 1. If P>1/3, ARH is less efficient than Huffman coding. 2. If 1/3/spl les/P>2/5, ARH is less than or equally efficient as Huffman coding, depending on the source distribution. 3. If 2/5/spl les/P/spl les/0.618, ARH and Huffman coding are equally efficient. 4. If P<0.618, ARH is more efficient than Huffman coding. We give examples of applying ARH coding to some specific sources.