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A method for bounding the rate of bit-stuffing encoders for 2-D constraints is presented. Instead of considering the original encoder, we consider a related one which is quasi-stationary. We use the quasi-stationary property in order to formulate linear requirements that must hold on the probabilities of the constrained arrays that are generated by the encoder. These requirements are used as part of a linear program. The minimum and maximum of the linear program bound the rate of the encoder from below and from above, respectively. A lower bound on the rate of an encoder is also a lower bound on the capacity of the corresponding constraint. For some constraints, our results lead to tighter lower bounds than what was previously known.