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A rigorous derivation is given of the coding rate of a variable-to-variable length bit-stuffing coder for a two-dimensional (1,∞)-constrained channel. The coder studied is "nearly" a fixed-to-fixed length algorithm. Then an analogous variable-to-variable length bit-stuffing algorithm for the three-dimensional (1,∞)-constrained channel is presented, and its coding rate is analyzed using the two-dimensional method. The three-dimensional coding rate is demonstrated to be at least 0.502, which is proven to be within 4% of the capacity.