Single-wall carbon nanotubes (SWNTs) have exceptional strength and stiffness and high thermal and electrical conductivity, making them excellent candidates for aerospace structural materials. However, one of the most fundamental challenges is purifying the SWNTs. The purpose of this study was to develop a simple purification process for SWNTs, along with an understanding of the purification process. In addition, uncomplicated analytical methods were sought to screen and compare various purification methods. In this study, we demonstrate an easy method of cleaning SWNTs and evaluating their purity. The cleaning method, which employed oxidative heat treatment followed by acid reflux, was straightforward, inexpensive, and fairly effective. The purification mechanism was determined to be, first, that much of the non-nanotube carbon and iron catalyst was oxidized and, second, that the acid washing removed the iron oxide, leaving relatively pure SWNTs. Also, it was shown that a combination of thermal gravimetric analysis and Raman spectroscopy, both of which take only a few minutes and require little sample preparation, are sufficient as qualitative screening tools to determine the relative purity of SWNTs. Other analytical techniques were used to verify the validity of the screening techniques.