Angular momentum constraints for coherently controlling chiral purification of racemic mixtures using the dipole-electric field interaction are examined in detail for two different scenarios. First shown is that achieving enantiomeric control in our earlier scheme [M. Shapiro, E. Frishman, and P. Brumer, Phys. Rev. Lett. 84, 1669 (2000)], using parallel laser pulses, requires that the system be M-polarized, where M is the projection of the total angular momentum along the axis of laser polarization. An alternate scenario is then introduced that allows chiral control in an unpolarized racemic mixture by using three mutually perpendicular linearly polarized light fields. Analytic expressions for the enantiomeric excess in both cases are derived and computational results are presented. (C) 2003 American Institute of Physics.