A central goal of modern materials physics and nanoscience is the control of materials and their interfaces to atomic dimensions. For interfaces between polar and nonpolar layers, this goal is thwarted by a polar catastrophe that forces an interfacial reconstruction. In traditional semiconductors, this reconstruction is achieved by an atomic disordering and stoichiometry change at the interface, but a new option is available in multivalent oxides: if the electrons can move, the atoms do not have to. Using atomic-scale electron energy loss spectroscopy, we have examined the microscopic distribution of charge and ions across the (001) LaAlO3/SrTiO3 interface. We find that there is a fundamental asymmetry between the ionically compensated AlO2/SrO/TiO2 interface, and the electronically compensated AlO2/ LaO/TiO2 interface, both in interfacial sharpness and charge density. This suggests a general strategy to design sharp interfaces, remove interfacial screening charges, control the band offset and, hence, markedly improve the performance of oxide devices.