In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space Lpa(G), 1 \u3c p \u3c 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces Dq, q \u3e 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on Lpa(), 1 \u3c p \u3c 2
