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Recent experiments on 12C + 24Mg and preliminary data on 12C + 26Mg show that we observe the hindrance phenomenon in these two systems that are close to the lighter ones relevant for astrophysics. The cross section at the hindrance threshold has a remarkably high value for 12C + 24Mg, while it is closer to an empirical systematics for 12C + 26Mg. The lowest-energy fusion cross sections of 12C + 24Mg are consistent with simple one-dimensional barrier penetration calculations, i.e. the coupling strengths seem to be strongly damped far below the barrier. Measurements at slightly lower energies would be essential to discriminate between different models and to allow reliably extrapolating to the lighter systems producing energy and elemental synthesis in stellar environments.