This paper addresses the problem of disturbance attenuation tin the sense of L-2-gain), with internal stability and no cost on the control input, for nonlinear systems, when the problem of almost disturbance decoupling is not solvable, i.e., when the least achievable attenuation level between disturbance and regulated output is nonzero. Two different approaches are provided, which facilitate the estimation of an upper bound for such a value.