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Abstract We analyze magnetic field data from two magnetosheath crossings, representative of a larger collection of similar cases in the database of the Cluster spacecraft. We apply a novel data analysis method to identify the power-law behavior of the structure functions and to find the validity range of the power-law scaling. We validate the technique with solar wind magnetic field data and a synthetic magnetic field signal. This approach grants a rigorous determination of the scale range for a linear fit of the structure function in the log–log representation, which most often is chosen arbitrarily. The fitting allows an estimation of the power spectral index from the scale variation of the second-order structure function exponent. Data recorded during the first Cluster magnetosheath crossing, called Event 1, indicate three different power-law scaling regimes (injection, inertial, and kinetic) separated by two spectral breaks, consistent with the scenario of fully developed turbulence. However, data from the second Cluster magnetosheath crossing, called Event 2, depict a different scenario with only two power-law scaling regimes determined from the fit. A spectral slope shallower than the Kolmogorovian solar wind power-law index is determined at magnetohydrodynamic scales, spanning more than three frequency decades, which is separated by a spectral break from the kinetic regime. An analysis of simultaneous solar wind data from the Advanced Composition Explorer suggests that the scale behavior of the magnetosheath fluctuations might be controlled by the structure of the bow shock; solar wind turbulent fluctuations are only partially destroyed while they are carried across the bow shock. Both events are recorded in a quasi-perpendicular magnetosheath.