Continuous-time Levy flights (CTLF) are reconsidered in the framework of non-separable continuous-time random walk (CTRW) model in order to properly treat the spatio-temporal relations in terms of the self-similar structure of the Levy process. Accordingly, a novel spatio-temporal coupling is introduced by assuming that in each order of the structure the probability density for the flight and that for waiting are joined. As a result of competition between flights and waitings an enhanced, dispersive or normal diffusion was recognized in distinction from the prediction of the commonly used separable CTRW model where, e.g., the enhanced diffusion is lost and dispersive one is strongly limited. This renewed CTLF approach offers a possibility to properly model the time-dependence for any fractional (critical) wandering of jump type, for example, it seems that the hydrogen diffusion in some metallic glasses or nanocompounds has chance to be described by our approach.