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This paper reexamines Jelinek's proof that tree codes can be used to approach the rate-distortion bound. It is shown that the branching process used in Jelinek's proof is not a (strict-sense) branching process (SSBP) when the source is asymmetric. Branching processes with random environments (BPWRE) are introduced and used to extend the proof to general discrete-time memoryless sources. The theory developed indicates why a particular metric used in experiments performed better than another suggested by the original proof.