The invention concerns a tyre tread comprising a rubber composition based on at least: (i) a diene elastomer; (ii) more than 60 wt. % parts of elastomer of a reinforcing inorganic filler; (iii) between 2 and 15 wt. % parts of elastomer of a coupling agent; (iv) between 4 and 12 wt. % parts of elastomer of a bismaleimide compound. Said tread has, after the tyre comprising it has been mechanically broken in, a rigidity gradient radially increasing from the surface towards the inside of the tread, providing the tyre with an improved adherence properties/ behaviour compromise. Such a tread is useful for making or retreading tyres. The invention also concerns tyres comprising such a running tread.