In this paper we consider the class of anti-uniform Huffman codes and derive tight lower and upper hounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. Also an upper bound on the entropy of AUH codes is also presented in terms of the average cost of the code. The Fibonacci distributions are introduced which play a fundamental role in AUH codes. It is shown that such distributions maximize the average length and the entropy of the code for a given alphabet size. Another previously known bound on the entropy for given average length follows immediately from our results.