A generalized eigenequation is derived for the optimal pairs of phase-unlocked pump-dump fields in the control of pure state molecular systems in the weak response regime. The associated eigenvalues are further correlated to the yields of pump-dump control, thus the globally optimal pair of phase-unlocked pump-dump fields is identified unambiguously. Presented is also a hierarchy of reduction from the general Liouville-space density matrix control formulation in the strong response regime to various linearized control equations in the weak response regime. Application to the control of a molecular ro-vibronic level in the ground electronic surface reveals a novel symmetry relation between the optimal pump field and its counterpart of the optimal dump field. (C) 1997 American Institute of Physics.