Practical considerations arising from Doppler distributions and beam divergence typically limit the amount of internal excitation that can be produced as a molecule passes across a cw laser beam. For coherent excitation this population transfer is furthermore limited by coherent population return (CPR), in which transiently excited molecules, off resonance, adiabatically evolve so as to return to the initial state at the end of a smooth pulse. We illustrate this effect with simulations, and show that in principle the presence of incoherence in the laser radiation (i.e., a finite bandwidth) can help suppress CPR, thereby substantially improving the averaged population transfer. For cases of practical relevance, the velocity-averaged population transfer can be optimized by a proper choice of the laser beam waist along the molecular beam direction. (C) 2003 American Institute of Physics.