The main assumption of the so-called ε-regularity theory of suitable weak solutions to the Navier-Stokes equations is uniform smallness of certain scale-invariant quantities, which rules out singularities. One of the best results of ε-regularity is the famous Caffarelli-Kohn-Nirenberg theorem. Our goal is to understand what happens if the assumption on smallness of scale-invariant quantities is replaced with their uniform boundedness. The latter makes it possible to use blow-up technique and ...