Individual single-wall carbon nanotubes (SWNTs) and double-wall carbon nanotubes (DWNTs) were suspended in water for optical studies using sodium-cholate and other surfactants. We used time-resolved photoluminescence (PL) spectroscopy to study the influence of tube chirality and diameter as well as of the environment on nonradiative decay in small diameter tubes. The studies provide evidence for PL from small diameter core tubes in DWNTs and for a correlation of nonradiative decay with tube diameter and exciton red shift as induced by interaction with the environment.