  We consider the effects of Distorted Gravity on the traversability of the
wormholes. In particular, we consider configurations which are sustained by
their own gravitational quantum fluctuations. The Ultra-Violet divergences
appearing to one loop are taken under control with the help of a Noncommutative
geometry representation and Gravity's Rainbow. In this context, it will be
shown that for every framework, the self-sustained equation will produce a
Wheeler wormhole, namely a wormhole of Planckian size. This means that, from
the point of view of traversability, the wormhole will be traversable in
principle, but not in practice. To this purpose, in the context of Gravity's
Rainbow we have considered different proposals of rainbow's functions to see if
the smallness of the wormhole is dependent on the chosen form of the rainbow's
function. Unfortunately, we discover that this is not the case and we suggest
that the self-sustained equation can be improved to see if the wormhole radius
can be enlarged or not. Some consequences on topology change are discussed.
