We review an extensive study of the factors that influence the intensity of coherent, nonlinear four-wave mixing (FWM) in carbon nanotubes, with particular attention to the variability inherent to single-walled carbon nanotubes (SWNTs). Through a combination of spatial imaging and spectroscopy applied to hundreds of individual SWNTs in optoelectronic devices, the FWM response is shown to vary systematically with free-carrier concentration. This dependence is manifested both in the intrinsic SWNT band structure and also by extrinsic and environmental effects. We demonstrate the sensitivity of the SWNT FWM signal by investigating SWNTs transferred from one substrate to another, before and after the introduction of chemical damage, and with chemical and electrostatic doping. The results demonstrate FWM as a sensitive technique for interrogating SWNT optoelectronic properties. © 2012 American Physical Society.