Using molecular dynamics simulations, we reveal ion rectification in charged nanocones with exit diameters of 1-2 nm. The simulations exhibit an opposite rectification current direction than experiments performed in conical channels with exit diameters larger than 5 nm. This can be understood by the fact that in ultranarrow charged cones screening ions are trapped close to the cone tip at both field directions, which necessitates them to be released from the cone in a correlated multi-ion fashion. Electroosmosis induced by a unidirectional ion flow is also observed.