Extensive control over enantiomer populations using achiral light is computationally demonstrated for J, M-J-selected 1,3 dimethylallene. In particular, by altering the detuning of one of three lasers incident on an J, M-J-polarized racemic mixture, one can alter the enantiomeric excess from approximate to 93% of the L enantiomer to approximate to 93% of the D enantiomer.