Treatment of carbon nanotubes by oxidizing acids is extensively used to dissolve metal residues from raw nanotube samples. The effect of acid treatment on the tubes themselves is twofold: it introduces uniform carboxylic sidegroups on the tube ends and defects, and it increases the overall charge concentration on the nanotube walls, thereby p-doping the material. Wide-range optical spectroscopy is an ideal tool to characterize both effects from one type of measurement: vibrational signatures indicate the presence of the sidegroups, the increase in far-infrared absorption signals the presence of free carriers, and the disappearance of interband transitions is the consequence of the depletion of Van Hove singularities when introducing holes. We have subjected carbon nanotube samples to two kinds of acid treatment: mild (in HNO3 vapor at room temperature) and aggressive (high-temperature reflux). We found that on mild treatment, electronic doping occurs without defect oxidation to carboxylic groups, while the aggressive procedure leads to both doping and defect oxidation. Our spectroscopic data unambiguously prove that the changes in electrical conductivity on acid doping are intrinsic, and not just a result of improving the contact between nanotubes.