Nanoscale memory devices, whose resistance depends on the history of the electric signals applied, could become critical building blocks in new computing paradigms, such as brain-inspired computing and memcomputing. However, there are key challenges to overcome, such as the high programming power required, noise and resistance drift. Here, to address these, we present the concept of a projected memory device, whose distinguishing feature is that the physical mechanism of resistance storage is decoupled from the information-retrieval process. We designed and fabricated projected memory devices based on the phase-change storage mechanism and convincingly demonstrate the concept through detailed experimentation, supported by extensive modelling and finite-element simulations. The projected memory devices exhibit remarkably low drift and excellent noise performance. We also demonstrate active control and customization of the programming characteristics of the device that reliably realize a multitude of resistance states.