The computation of information rate regions remains a challenging problem.  Distributed encoding and communication problems are increasingly important, and many bounds on achievable rate regions have been derived.  We present extensions of the methods of Blahut and Arimoto that facilitate computation of such rate regions.  A general theory that computes distributions that optimally trade off values of mutual information is presented.  We show computational results for lossless encoding with compressed side information and for information embedding problems.