The scaling of dry thermal oxides into the thin (<400 Å) range continues to motivate studies of the rapid initial oxidation rate of silicon unaccounted for by a linear-parabolic model. In this paper, silicon oxidation kinetics in this unresolved regime are studied by the incremental reoxidation of thin thermally grown and deposited silicon oxide layers on silicon. It is found that the reoxidation rates of thermally grown oxides in the thin regime rapidly decrease with increasing oxide thickness. In contrast, the reoxidation rates of deposited oxides are faster, and nearly thickness independent. It is also found that the reoxidation rates of thin thermal oxides can be significantly increased by inert thermal annealing. Existing thin-regime oxidation models are evaluated in light of these experimental findings, and it is concluded that only models invoking stress suppression of early oxidation kinetics can reconcile all experimental observations. In further support of a stress argument, the time and temperature effects of inert annealing are shown to be quantitatively consistent with a Maxwellian model for stress relaxation. Kinetic parameters extracted from experimental data are utilized to isolate specific mechanisms for the suppression of oxidation rate during the initial stages of silicon oxidation.