We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa.The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.3/2 rms ∆γ/ R 1/2 E * where E * is the plane strain elastic modulus, ∆γ is interface energy. The choice of R seems critical in view of its sensitivity to "resolution" or "magnification" [13], i.e. on the shortest wavelength in the roughness spectrum. In the "fractal limit", i.e. for an infinite number of wavelength R → 0, there would be no stickiness for any surface, irrespective of the geometrical characteristics, like fractal dimension, or root mean square heigths (rms) amplitude. Hence, FT apparent good correlation with the theory despite the many limitations (see [14]), may have been due to a fortuitous choice of R at a