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A class of spectral sub-grid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of sub-grid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale extension where anomalous exponents are measured by roughly one order of magnitude, when compared to direct numerical simulations or to other popular sub-grid closures atthe same  resolution. As a result, one can achieve an extreme high accuracy in the determination of the scaling properties with a computational effort that decreases by three orders of magnitude compared to any approach based on direct numerical simulations of the full equations. Aside from the unprecedented improvement in the precision of inertial range statistics, our study contributes to clarify  the robustness of turbulent flows with respect to  small-scale closures and opens the way to apply similar protocols to many other configurations, e.g. in stratified media, under rotation, along the homogeneous directions in bounded  domains or even for notoriously stiff problems as the kinematic dynamo in the limit of small Prandtl numbers.