Landauer’s erasure principle states that the irreversible erasure of a one-bit memory, embedded in a thermal environment, is accompanied with a work input of at least kTln2. Fundamental to that principle is the assumption that the physical states representing the two possible logical states are close to thermal equilibrium. Here, we propose and theoretically analyze a minimalist mechanical model of a one-bit memory operating with squeezed thermal states. It is shown that the Landauer energy bound is exponentially lowered with increasing squeezing factor. Squeezed thermal states, which may naturally arise in digital electronic circuits operating in a pulse-driven fashion, thus can be exploited to reduce the fundamental energy costs of an erasure operation.