This article explores the influence of permanent dipole moments, i.e., of direct vibrational excitations, on the dynamical dissociation quenching (DDQ) effect, a mechanism for laser-induced vibrational trapping in the infrared (IR) spectral range which was recently demonstrated for the homonuclear H-2(+) ion, and was shown to result from a proper synchronization of the molecular motions with the oscillations of the laser electric field [see F. Chateauneuf, T. Nguyen-Dang, N. Ouellet, and O. Atabek, J. Chem. Phys. 108, 3974 (1998)]. To this end, the wave packet dynamics of the HD+ and, to a lesser extent, the HCl+ molecular ions are considered in an intense IR laser field of variable frequency. Variations in the absolute phase of the laser electric field, a form of variations in the initial conditions, reveal new signatures of the DDQ effect due to the presence of nonzero permanent dipole moments in these molecules. The added permanent dipole/field interaction terms induce a discrimination between parallel and antiparallel configurations of the aligned molecule with respect to the laser＇s instantaneous electric field. As a result, molecules that are prepared antiparallel to the field at peak intensity find their dissociation quenched most efficiently, while those that are prepared parallel to the field are strongly dissociative.