An algorithm for the minimum-redundancy encoding of a discrete information source is proposed. In the case of memoryless sources it is shown that the theoretical compression can be appmached within any desired threshold without the burden of alphabet extensions (i.e., the encodhg of blocks ofLprimary symbols) and also irrespective of 1) the primary and secondary alphabet sizes 2) the numerical values of primary symbol probabillties, and 3) the order and structure of the encoding tree. The same algorithm is then extended to sources with memory and to cases in which there is a constraint on the statistical description of the secondary sequence (e.g., secondary symbol probabilities are given). The technique can thus be used to transform any given discrete source into any other given discrete source while minimizing the ratio of average secondary sequence length to average primary sequence length.