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It is well known that if $G$ is a countable amenable group and $G\curvearrowright (Y, \nu)$ factors onto $G \curvearrowright (X, \mu)$, then theentropy of the first action must be greater than or equal to the entropy of thesecond action. In particular, if $G \curvearrowright (X, \mu)$ has infiniteentropy, then the action $G \curvearrowright (Y, \nu)$ does not admit anyfinite generating partition. On the other hand, we prove that if $G$ is acountable non-amenable group then there exists a finite integer $n$ with thefollowing property: for every probability-measure-preserving action $G\curvearrowright (X, \mu)$ there is a $G$-invariant probability measure $\nu$on $n^G$ such that $G \curvearrowright (n^G, \nu)$ factors onto $G\curvearrowright (X, \mu)$. For many non-amenable groups, $n$ can be chosen tobe $4$ or smaller. We also obtain a similar result with respect to continuousactions on compact spaces and continuous factor maps.

Every action of a non-amenable group is the factor of a small action