We have developed a microwave-assisted, reagent-free method for the efficient primary purification of MW and SW carbon nanotubes that is extremely fast compared to previously reported processes. The treatment dissociates and disperses non-nanotube carbon in an organic solvent to yield very pure carbon nanotubes within a few minutes of heating and a simple filtration, without the involvement of acidic/oxidative reagents. According to thermogravimetric analysis, Raman and IR spectroscopy, as well as scanning and transmission electron microscopy, the process yields pure nanotubes with a low degree of defects.