The impact of rotating magnetic islands on background radial profiles in the presence of strong turbulent transport is analysed, with particular emphasis on island widths of the order of 6 − 10 ion Larmor radii. Only the case of ion temperature gradient (ITG) turbulence is considered. A significant reduction of fluctuations is found when island and turbulence co-rotate and the island width is of the order of the radial correlation length of turbulence. This reduction is not due to a flattening of ion temperature, suggesting an additional mechanism. A nonlinear transfer of energy from small to large scale structures might be responsible for the stabilization at a scale close to the radial correlation length of turbulence. It is shown that in the presence of intermediate magnetic islands rotating in the ion diamagnetic direction the density flattening survives the radial turbulent transport, representing a destabilizing effect for a magnetic island in terms of bootstrap current. However, this flattening is not necessarily due to an adiabatic response of trapped ions. Owing to the fast parallel motion of electrons, their temperature is always flattened. Finally, when the island width is large enough (island width greater than 18 ion Larmor radii), the standard profile flattening leading to a linear stabilization of turbulence dominates over the other mechanisms.