ABSTRACT: We study the problem of perturbation of elliptic operators in rough domains. Given two operators L0 = ‒ div(A0∇.) and L = ‒ div(A∇.), we look for conditions in the discrepancy between A0 and A that allow us to transfer good properties from one operator to the other. For instance, we are interested in the fact that their elliptic measures belong to the class A∞. We extend the result of Fefferman-Kenig-Pipher to 1-sided CAD domains. This is, assuming a Carleson measure condition in the discrepancy between both matrices, we show that one of the elliptic measures belongs to A∞ if the same property holds for the other. To prove this result we will present two independent methods that are different from the one used by Fefferman-Kenig-Pipher. The first method uses the “bootstrapping of Carleson measures” technique, and it requires to consider the “small perturbation” case. The second method is a new approach that relies on the property that every bounded weak solution of a given operator satisfy Carleson measure estimates.