We have recently proposed a laser control scheme for ultrafast absorption in multilevel systems by parallel transfer (J. Phys. Chem. Lett. 2015, 6, 1724). In this work we develop an analytical model that better takes into account the main features of electronic absorption in molecules. We show that the initial vibrational coherence in the ground electronic state can be used to greatly enhance the rate and yield of absorption when ultrashort pulses are used, provided that the phases of the coherences are taken into account. On the contrary, the initial coherence plays no role in the opposite limit, when a single long pulse drives the optical transition. The theory is tested by numerical simulations in the first absorption band of Na-2.