Huffman’s well-known coding method constructs a minimum redundancy code which minimizes the expected value of the word length. In this paper, we characterize the minimum redundancy code with the minimum variance of the word length. An algorithm is given to construct such a code. It is shown that the code is in a certain sense unique. Furthermore, the code is also shown to have a strong property in that it minimizes a general class of functions of the minimum redundancy codes as long as the functions are nondecreasing with respect to the path lengths from the root to the internal nodes of the corresponding decoding trees.