High-quality, blue-violet digital spectroscopy has been assembled of most previously known (and one new) members of the O3 class that exhibit N iv emission and N v absorption lines, with the collaboration of most specialists in the field. A detailed comparative study has led to the introduction of new spectral types O2 and O3.5 to describe the range of classification criteria present. Primary reliance has been placed on the N iv/N iii selective emission-line ratio, because of various difficulties affecting the interpretation of weak He i absorption lines in some of these spectra, which are discussed. Some representative spectra defining the new types are shown. The majority of the O2 - O3 class members reside in the LMC. Their large ranges of luminosities and masses suggest a close evolutionary connection to the WN class, as do several spectroscopic and spatial relationships. The salient characteristics of O2-O3 spectra in the ultraviolet longward of 1200 Å have been established for some time by IUE and HST data. Recently, the rich 900-1200 Å range has been well covered for the first time by FUSE; in a collaboration with its hot-star team, a comprehensive atlas of OB spectra in the Magellanic Clouds has been prepared. Several O2 stars are included, one of which is newly discovered, and some examples of these data are also shown.