The selectivity of ion transport in nanochannels is of primary importance for a number of physical, chemical, and biological processes ranging from fluid separation to ion-channel-regulated cellular processes. Fundamental understanding of these phenomena requires model nanochannels with well-defined and controllable structural properties. Carbon nanotubes provide an ideal choice for nanofluidic studies because of their simple chemistry and structure, the atomic scale smoothness and chemical inertness of the graphitic walls, and the tunability of their diameter and length. Here, we investigate the selectivity of single and, for the first time, binary salt mixtures transport through narrow carbon nanotubes that act as the only pores in a silicon nitride membrane. We demonstrate that negatively charged carboxylic groups are responsible for the ion rejection performance of carbon nanotube pores and that ion permeation of small salts can be tuned by varying solution pH. Investigation of the effect of solution composition and ion valences for binary electrolytes with common cation in a pressure-driven flow reveals that the addition of slower diffusing multivalent anions to a solution of faster diffusing monovalent anions favors permeation of the monovalent anion. Larger fractions and valences of the added multivalent anions lower the rejection of the monovalent anion. In some cases, we observe negative rejection at low monovalent ion content.