As previously demonstrated, a single hole is sufficient to markedly reduce the fracture strength of a carbon nanotube (CNT). Herein we present calculations exploring the effects of multiple holes on the modulus, fracture strength, and fracture strain of CNTs. The modulus decreases sharply and approximately linearly as a function of the pitting density. A few holes cause a decrease in the failure strain but extensive pitting leads to higher failure strains. These results suggest that the unusually low modulus measurements and high failure strains reported in the experiments of Yu et al. [Science 287 (2000) 637] were a consequence of purification induced oxidative pitting.