Control of quantum tunneling by external driving fields is a subject of major relevance in different linear and nonlinear dynamical systems. The driven double-well (bistable) potential has provided since more than one decade a simplified and paradigmatic model to investigate the dynamics underlying tunneling control in such diverse physical systems as cold atoms in optical traps, superconducting quantum interference devices, and multi-quantum dots. As for strong driving at a frequency close to the classical frequency at the bottom of each well one observes chaos-assisted tunneling enhancement, at lower frequencies and for certain ratios between frequency and amplitude of the driving field tunneling can be suppressed, as originally proposed in a famous work by Grossman, Hanggi and coworkers [1]. Such a phenomenon is nowadays referred to as" coherent destruction of tunneling"(CDT). In spite of the great …