Direct laser vaporization of transition-metal/graphite composite rods produced single-walled carbon nanotubes (SWT) in the condensing vapor in a heated flow tube. A much higher yield of nanotubes was found, with little of the amorphous overcoating on those produced by the metal-catalyzed arc-discharge method. A number of parameters were varied to achieve the highest yield. A mixture of Co with Ni catalyzed about 50% of all the carbon vaporized to SWT. A model for SWT growth is presented for both the present case and the arc.