We consider combined stimulated Raman adiabatic passage (STIRAP) and fast-forward field (FFF) control of selective vibrational population transfer in a polyatomic molecule. The motivation for using this combination control scheme is 2-fold: (i) to overcome transfer inefficiency that occurs when the STIRAP fields and pulse durations must be restricted to avoid excitation of population transfers that compete with the targeted transfer and (ii) to overcome transfer inefficiency resulting from embedding of the actively driven subset of states in a large manifold of states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP and FFFs that do not individually generate processes that are competitive with the desired population transfer can generate greater population transfer efficiency than can ordinary STIRAP with similar field strength and/or pulse duration.