It is well known that if G is a countable amenable group and G (Y , ν) factors onto G (X , µ), then the entropy of the first action must be at least the entropy of the second action. In particular, if G (X , µ) has infinite entropy, then the action G (Y , ν) does not admit any finite generating partition. On the other hand, we prove that if G is a countable nonamenable group then there exists a finite integer n with the following property: for every probability-measure-preserving action G (X ,

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... ) there is a G-invariant probability measure ν on n G such that G (n G , ν) factors onto G (X , µ). For many nonamenable groups, n can be chosen to be 4 or smaller. We also obtain a similar result with respect to continuous actions on compact spaces and continuous factor maps.