The buried oxide (BOX) layers of SIMOX structures produced by oxygen ion implantation are confined between the Si substrate and top Si layer. Their charge trapping properties, as affected by various treatments in the presence or absence of the confining top Si layer, were studied. The BOX of most of the SIMOX samples we have studied contain electron traps related to excess silicon in the form of clusters about 1-4 nm in size. In contrast, unconfined oxides, such as thermally grown SiO2 films and the so-called "equilibrium oxide" prepared by oxygen ion implantation to such a thickness that all of the top Si layer is consumed, do not contain these traps. The density of traps with a relatively small capture cross section in confined BOX layers can be reduced by implanting supplemental oxygen into the completed SIMOX structure. However, the traps with relatively large cross section are only slightly affected, despite a significant increase in the oxide thickness. In contrast, traps can be completely eliminated by an oxidizing heat-treatment without measurable additional oxide growth if the structure is unconfined, i.e., the top Si layer is removed. It is suggested that the confinement effect is related to the structure of the noncrystalline BOX layer which is affected by the confining Si layers. This effect stabilizes the traps, particularly those with a large cross section, which are near the S1/BOX interface(s).