While the purification of carbon nanotubes may be considered as an already sorted matter, their use in some highly demanding fields such as electrochemistry, biological studies or magnetism may be precluded by the remaining catalyst and carbonaceous impurities. For these purposes, the widely-used purification methods need to be improved. In this paper, a comprehensive study of the well-known gas-phase purification procedure of single wall nanotubes (SWNTs) is performed, which aims at depicting the nature and the amount of the remaining impurities, of both the catalyst and carbon types, and at getting insights into its mechanism. This has been achieved by cross-referencing data emerging from transmission electron microscopy (TEM), electron energy loss spectroscopy (EELS), electron diffraction, magnetization measurements, X-ray diffraction (XRD) and Raman spectroscopy. We demonstrate that this method can lead to the elimination of the largest part of the impurities while maintaining fairly good yields. According to the mechanistic picture we have drawn, we suggest some possible improvement to the procedure that should lead to fully purified SWNTs with limited subsequent losses.