Using (+)-3-(trifluoroacetyl)camphor, or R(+)- and S(-)-3-methoxy-3-phenyl-4,4,4-trifluoro-butan-2-one as precursors for chiral dioxiranes generated in situ, the asymmetric epoxidation of prochiral alkenes trans-beta-methylstyrene, trans-2-octene, and cis-2-methyl-7-octadecene has been achieved in 12-20% ee.