We show that perturbation produced by coupling a triple well tunneling system to a harmonic mode can generally reduce tunneling duration as the coupling strength increases, although in the weak coupling regime, it may also cause tunneling-delay. A periodically varying well-depth is predicted to enhance tunneling duration in a triple well and create a 'resonance-like' suppression of tunneling at a critical frequency (omega(c)) of oscillation. (c) 2006 Elsevier B.V. All rights reserved.