The dianion of methyl acetoacetate is alkylated at the γ-carbon with homoallylic bromides. The resulting alkenes are epoxidized and then cyclized with a Lewis acid to produce esters of 6,8-dioxabicyclo[3.2.1]octane. These esters can be hydrolyzed and decarboxylated in a novel reaction. This methodology has been applied to a stereospecific synthesis of the title compounds. In addition, one of the intermediates in the exo-brevicomin synthesis can be resolved to provide the natural (+)-pheromone.