We report the realization and characterization of independently controllable tunnel barriers within a carbon nanotube. The nanotubes are mechanically bent or kinked using an atomic force microscope, and top gates are subsequently placed near each kink. Transport measurements indicate that the kinks form gate-controlled tunnel barriers, and that gates placed away from the kinks have little or no effect on conductance. The overall conductance of the nanotube can be controlled by tuning the transmissions of either the kinks or the metal-nanotube contacts.