We have examined the sensitivity to the presence of background states of population transfer to a predissociating molecular state generated by coherent two-pulse excitation. The system studied is intended to model optical control of the formation of a product in a photofragmentation reaction. The model spectrum of states is a generalization of the three-state spectrum considered in the conventional STIRAP method in three respects: the target state is a resonance in the continuum, the spectrum includes both unoccupied background states that have finite lifetimes and some unoccupied pairs of background states that are in resonance with the excitation pulses, and nonadiabatic population transfer is allowed. We examine the variation of the population transfer to the target state with respect to its lifetime, as well as the robustness of the population transfer with respect to variation of the area of overlap of the two excitation pulses and with respect to the presence of background states (some of which have finite lifetimes). Our results show that there is a broad range of conditions under which it is possible to transfer population efficiently from an initial state to a target predissociating state using coherent two-pulse excitation, although that population transfer is not always adiabatic.