  We consider a Navier-Stokes-Voigt fluid model where the instantaneous
kinematic viscosity has been completely replaced by a memory term incorporating
hereditary effects, in presence of Ekman damping. The dissipative character of
our model is weaker than the one where hereditary and instantaneous viscosity
coexist, previously studied by Gal and Tachim-Medjo. Nevertheless, we prove the
existence of a regular exponential attractor of finite fractal dimension under
rather sharp assumptions on the memory kernel.
