Abstract. We study backward extensions of 2-variable weightedshifts with nite atomic Berger measure. We provide a necessaryand sucient condition for the subnormality of such extensions.As an application, we give a simple counterexample for the Curto-Muhly-Xia conjecture [10]. 1. IntroductionLet Hbe a complex Hilbert space and let B(H) denote the algebraof bounded linear operators on H. We say that T2B(H) is normal ifTT= TT, subnormal if T= Nj H , where Nis normal and N(H) H,and hyponormal if TTTT. For S;T2B(H), let [S;T] := ST TS.We say that an n-tuple T = (T 1 ; ;T n ) of operators on His (jointly)hyponormal if the operator matrix[T;T] :=0BBB@[T 1 ;T 1 ] [T 2 ;T 1 ] [T n ;T 1 ][T 1 ;T 2 ] [T 2 ;T] [T n ;T]......... ...[T 1 ;T n ] [T 2 ;T n ] [T n ;T n ]1CCCAis positive semide nite on the direct sum of ncopies of H(cf. [1], [2],[10], [14]). The n-tuple T is said to be normal if T is commuting andeach T i is normal, and T is subnormal if T is the restriction of a normaln-tuple to a common invariant subspace. Clearly, normal )subnormal)hyponormal.