  We study the effects of scattering lengths on L\'evy walks in quenched
one-dimensional random and fractal quasi-lattices, with scatterers spaced
according to a long-tailed distribution. By analyzing the scaling properties of
the random-walk probability distribution, we show that the effect of the
varying scattering length can be reabsorbed in the multiplicative coefficient
of the scaling length. This leads to a superscaling behavior, where the
dynamical exponents and also the scaling functions do not depend on the value
of the scattering length. Within the scaling framework, we obtain an exact
expression for the multiplicative coefficient as a function of the scattering
length both in the annealed and in the quenched random and fractal cases. Our
analytic results are compared with numerical simulations, with excellent
agreement, and are supposed to hold also in higher dimensions
