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Source distributions that can be encoded with zero redundancy for the case of unequal code symbol costs are examined. These distributions provide a natural generalization of the binary, equal costs case for which these distributions are the dyadic distributions. These zero redundancy codes have the property that the expected proportion of codeword symbols given by a particular letter is equal to an exponential function of the code letter cost. The converse is not true in general, however partial converse results hold. Maximum-entropy zero-redundancy distributions are easily identified through their connection with unequal cost coding for uniform sources.

Conditions on the probability distributions of two sources that describe their relative uniformity are shown to be sufficient for inequalities on their minimum average codeword lengths and entropies. The Huffman coding problem and variants involving Renyi entropy are addressed.