For discrete-time plants with unknown dead-zones at the output we propose a new controller structure with an adaptive dead-zone inverse. We consider two control problems; one when only the dead-zone is unknown, and the other when the whole plant is unknown. We allow the dead-zone to be with unequal slopes. The proposed controller structure results in a linear parametrization which is crucial for developing adaptive update laws. We prove the signal boundedness for the closed-loop system, and for a special case we establish asymptotic tracking. Simulation results show that our adaptive control schemes improve system performance.