Two familiar notions of correlation are re-discovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is  generated  based only on a description of the channel input. Wynerpsilas ldquocommon informationrdquo coincides with the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannonpsilas mutual information. This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.