The reactions of alkyl peroxy radicals (RO2) play a central role in the low-temperature oxidation of hydrocarbons. In this work, we present high-pressure rate estimation rules for the dissociation, concerted elimination, and isomerization reactions of RO2. These rate rules are derived from a systematic investigation of sets of reactions within a given reaction class using electronic structure calculations performed at the CBS-QB3 level of theory. The rate constants for the dissociation reactions are obtained from calculated equilibrium constants and a literature review of experimental rate constants for the reverse association reactions. For the concerted elimination and isomerization channels, rate constants are calculated using canonical transition state theory. To determine if the high-pressure rate expressions from this work can directly be used in ignition models, we use the QRRK/MSC method to calculate apparent pressure and temperature dependent rate constants for representative reactions of small, medium, and large alkyl radicals with O-2. A comparison of concentration versus time profiles obtained using either the pressure dependent rate constants or the corresponding high-pressure values reveals that under most conditions relevant to combustion/ignition problems, the high-pressure rate rules can be used directly to describe the reactions of RO2.