LetG be a finitely-generated group of non-singular measurable transformations of a measure space (X, β,p). FixA∈β withp(A)>0. A general technique for groups gives sufficient conditions for there to exist aG-invariant measure ν equivalent top with ν((A)=1. These conditions are phrased in terms of the growth behavior ofg→p(gB) forB∈β. The question of necessity is handled in some special cases.