  It has been shown by van den Berg and Steif that the sub-critical Ising model
on $\mathbb{Z}^d$ is a finitary factor of a finite-valued i.i.d. process. We
strengthen this by showing that the factor map can be made to have finite
expected coding volume (in fact, stretched-exponential tails), answering a
question of van den Berg and Steif. The result holds at any temperature above
the critical temperature. An analogous result holds for Markov random fields
satisfying a high-noise assumption and for proper colorings with a large number
of colors.
