Given a Cayley graph for a non-amenable group, can one find a factor of an IID process that gives a random forest in which the average degree is greater than 2? Gaboriau-Lyons proved that the answer is `yes’ and this has interesting applications to ergodic theory. However, they required a lower bound on the entropy of the IID process. I’ll show, via random interlacements, how to remove this restriction. One application is that every IID process is a factor of every (nontrivial) IID process.