We present a numerical model for the prediction of the rough contact mechanics of a viscoelastic block, with graded rheology, in steady sliding contact with a randomly rough rigid surface. In particular, we derive the effective surface response of a stepwise or continuously-graded block in the Fourier domain, which is then embedded in a Fourier-based residuals molecular dynamic formulation of the contact mechanics. Finally we discuss on the role of small-scale wavelengths on rubber friction and contact area, and we demonstrate that the rough contact mechanics exhibits effective interface properties which converge to asymptotes upon increase of the small-scale roughness content, when a realistic rheology of the confinement is taken into account.We consider the case of a rigid, periodically-rough surface (of L 0 periodic length, in both x-and y-direction, with small wavelength cut-off frequency q 0 = 2π/L 0 ) in steady sliding adhesionless contact with a graded body characterized by linear rheology, under isothermal and frictionless conditions. We assume the small deformation regime to apply,