A spherical micelle of C12E6 is simulated at different pressures, from 0.001 to 3 kbar, by molecular dynamics. On increasing the pressure the alkyl tails of the surfactants pack tightly and stretch. At 3 kbar we observe dynamical slowing down of the oil core of the micelle. At that pressure the core is characterized by a high oil density, p(oil) approximate to 0.85 g/cm(3), regular density oscillation, and low chain entropy. Pressure affects the interfacial region as well. Dehydration, induced by the collapse of the hydrophilic head groups, is observed in the inner part of the interface. Such dehydration resembles temperature dehydration but differs in details. Our results support the interpretation of recent experiments on micellar solutions at high pressure.