  We analyze from a classical and quantum point of view the behavior of the
universe close to a little rip, which can be interpreted as a big rip sent
towards the infinite future. Like a big rip singularity, a little rip implies
the destruction of all bounded structure in the Universe and is thus an event
where quantum effects could be important. We present here a new phantom scalar
field model for the little rip. The quantum analysis is performed in quantum
geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We
find that the little rip can be avoided in the sense of the DeWitt criterion,
that is, by having a vanishing wave function at the place of the little rip.
Therefore our analysis completes the answer to the question: can quantum
cosmology smoothen or avoid the divergent behavior genuinely caused by phantom
matter? We show that this can indeed happen for the little rip, similar to the
avoidance of a big rip and a little sibling of the big rip.
