Four rate-limiting processes for the formation of single-wall carbon nanotubes (SWCNT) could be identified by varying furnace temperature, gas type, and pressure in a pulsed-laser evaporation setup. One rate-limiting process accounts essentially for all relevant gas-pressure dependencies and can be quantitatively described using a single gas-specific constant. One thermally activated process is related to fullerene formation, whereas another process, following a T-2-law, is discussed in terms of the diffusion of carbon through molten catalyst nanoparticles. The data provide strong support for an "undercooled melt" mechanism of nanotube formation.