  Consider the set of source distributions within a fixed maximum relative
entropy with respect to a given nominal distribution. Lossless source coding
over this relative entropy ball can be approached in more than one way. A
problem previously considered is finding a minimax average length source code.
The minimizing players are the codeword lengths --- real numbers for arithmetic
codes, integers for prefix codes --- while the maximizing players are the
uncertain source distributions. Another traditional minimizing objective is the
first one considered here, maximum (average) redundancy. This problem reduces
to an extension of an exponential Huffman objective treated in the literature
but heretofore without direct practical application. In addition to these, this
paper examines the related problem of maximal minimax pointwise redundancy and
the problem considered by Gawrychowski and Gagie, which, for a sufficiently
small relative entropy ball, is equivalent to minimax redundancy. One can
consider both Shannon-like coding based on optimal real number ("ideal")
codeword lengths and a Huffman-like optimal prefix coding.
