  Dark energy of phantom or quintessence nature with an equation of state
parameter $w$ almost equal to -1 often leads the universe evolution to a
finite-time future singularity. An elegant solution to this problem has been
recently proposed \cite{frampton11} under the form of the so-called Little Rip
cosmology which appears to be a realistic alternative to the $\Lambda$CDM
model. A viscous Little Rip cosmology is here proposed. Whereas generically
bulk viscosity tends to promote the Big Rip, we find that there are a number of
situations where this is not the case and where the formalism nicely adjusts
itself to the Little Rip scenario. We prove, in particular, that a viscous
fluid (or, equivalently, one with an inhomogeneous (imperfect) equation of
state) is perfectly able to produce a Little Rip cosmology as a purely
viscosity effect. The possibility of its induction as a combined result of
viscosity and a general (power-like) equation of state is also investigated in
detail. To finish, a physical, inertial force interpretation of the dissolution
of bound structures in the Little Rip cosmology is presented.
