The injection of charge carriers into pi-conjugated semiconductors, whether by electrochemical injection or chemical charge transfer, is a powerful approach to tune their electrical conductivity. Recently, the concept of dielectric catastrophe, where the charge carrier density is sufficiently large to significantly alter the intrinsic dielectric properties, has been demonstrated at high doping levels in organic semiconductor thin films. The observed increase in the dielectric constant leads to reduced coulombic interactions between charge carriers and the associated counterions, promoting enhanced free carrier generation and transport.Here, we employ a combination of steady state optical spectroscopy, quantitative 19F NMR studies, and microwave dielectric loss spectroscopy to probe charge carrier density and transport in doped single-walled carbon nanotube dispersions. We demonstrate that a similar dielectric catastrophe phenomenon can be observed even in isolated single-walled carbon nanotubes dispersed in a low dielectric constant solvent AND, perhaps more surprisingly, at carrier densities less than one carrier per nanotube. The precise details of the observed changes in complex dielectric function are dependent on the chemical structure of the charge-transfer dopant, with a near-instantaneous increase in the dielectric constant and electrical conductivity observed for low carrier densities using bulky benzyloxy-substituted icosahedral dodecaborane cluster dopants, DDBs. We attribute the observations to weak coulombic interactions between the injected charge carrier and the dopant counterion, along with the large polarizability afforded by the unique physicochemical properties of single-walled carbon nanotubes. If time permits, we will show results from recent studies where we extend this approach to the doping of other nanocarbons.