Oxidizable contaminants in water are destroyed quickly and efficiently by exposing a contaminated water flow to oxidizing conditions under pressure. Specifically, ozone generated from oxygen and hydrogen peroxide are injected into the water flow in at least one, and preferably more than one, high intensity mixing/reaction stage. The ozone and hydrogen peroxide are injected at velocities and directions approximately matching those of the contaminated water flow. High intensity mixing under pressure facilitates rapid and complete oxidation of the contaminants with minimal stripping of volatile contaminants and waste of undissolved ozone. Residual ozone levels after high intensity mixing are carefully monitored and minimized by adjusting the injection of hydrogen peroxide and ozone in order to suppress the formation of bromate.