The comparison of the results of direct numerical simulations of isotropic turbulence of Newtonian and viscoelastic fluid, based on the FENE-P model, provide evidence that viscoelasticity modifies qualitatively the behavior of the smallest scales: we observe a k−6 law in the far dissipation range of the energy spectrum and we show that it is a robust feature, roughly independent of the large-scale dynamics. It is further shown that the drag-reduction in such flows, as measured by the difference in energy dissipation between Newtonian and viscoelastic flow, strongly depends on the initial conditions.