In the present paper, a comprehensive self-consistent three-dimensional model is used to analyze physical aspects of the operation of oxide-confined vertical-cavity surface-emitting diode lasers (VCSELs) and to optimize their structures. The impact of the built-in radial confining mechanisms created by oxide apertures, i.e., the influence of their diameters and localizations on radial confinements of both the current injection into VCSEL active regions and electromagnetic fields of successive cavity modes, has been investigated. Basically, there are two extreme cases: the index-guided (IG) VCSELs with the aperture localized at the antinode position of the optical standing wave, characterized by a very low lasing threshold but exhibiting rather poor mode selectivity, and the gain-guided (GG) VCSELs with the aperture shifted to the node position, ensuring usually the single-fundamental-mode operation, but at the expense of much higher lasing threshold. In the present paper, the separate-confinement-oxidation VCSEL structure has been proposed exhibiting simultaneously advantages of both the IG VCSELs (the low lasing threshold) and the GG ones (the single-fundamental-mode operation).