Ketohydroperoxides (KHPs) are oxygenates with carbonyl and hydroperoxy functional groups, and they are generated under combustion and atmospheric conditions. Their fate is crucial for secondary organic aerosol formation in the troposphere and for the ignition processes of biofuels in advanced combustion engines. We investigated the thermodynamics and kinetics of nine hydrogen abstraction reactions from four ether KHPs by OH. We find that the rate constants are strongly affected by entropic effects whose estimation requires a consideration of higher-energy conformers of the transition state. A density functional was selected for these reactions by comparison to coupled cluster calculations, and it was used for calculations by multistructural canonical transition-state theory with multidimensional tunneling over the temperature range of 200-2000 K. We find that the effect of multistructural torsional anharmonicity is very large and quite different for the various ether KHP reactions. A leading cause of the structural dependence is the dominance of entropic factors due to the lack of hydrogen bonding in some of the higher-energy conformers of the transition states. Four of the reactions involve abstraction from the α-carbon (the carbon vicinal to the hydroperoxide group); they exhibit nonmonotonic temperature dependence with complex fuel-specific dependence. The rate constants for abstraction from a non-α-carbon of a given KHP can be faster than the ones for abstraction from an α-carbon; in two cases, this is due to entropy, and in one case, the non-α-carbon abstraction has a lower energy barrier. Tunneling and recrossing effects are also found to be important.