Materials exhibiting reversible resistive switching in electrical fields are highly demanded for functional elements in oxide electronics. In particular, multilevel switching effects allow for advanced applications like neuromorphic circuits. Here, we report a structurally driven switching mechanism involving the so-called "dead" layers of perovskite manganite surfaces. Forming a tunnel barrier whose thickness can be changed in monolayer steps by electrical fields, the switching effect exhibits well-defined and robust resistive states.