It has long been conjectured that the difficulty of heterogeneously epoxidizing higher alkenes such as propene is due to the presence in the molecule of "allylic" H atoms that are readily stripped off by the oxygenated surface of the metal catalyst resulting in combustion. Here, taking advantage of the intrinsically higher epoxidation selectivity of Cu over Ag under vacuum conditions, we have used three phenylpropene structural isomers to examine the correlation between adsorption geometry and oxidation chemistry. It is found that under comparable conditions alpha-methylstyrene, trans-methylstyrene, and allylbenzene behave very differently on the oxygenated Cu(111) surface: the first undergoes extensive epoxidation accompanied by relatively little decomposition of the alkene; the second leads to some epoxide formation and extensive alkene decomposition; and the third is almost inert with respect to both reaction pathways. This reactive behavior is understandable in terms of the corresponding molecular conformations determined by near-edge X-ray absorption fine structure spectroscopy and density functional theory calculations. The proximity to the surface of the C=C function and of the allylic H atoms is critically important in determining reaction selectivity. This demonstrates the importance of adsorption geometry and confirms that allylic H stripping is indeed a key process that limits epoxidation selectivity in such cases.