  We show that an appropriate choice of the potential parameters in
one-dimensional quantum systems allows for unity transmission of the tunneling
particle at all incident tunneling energies, except at controllable exceedingly
small incident energies. The corresponding dwell time and the transmission
amplitude are indistinguishable from those of a free particle in the
unity-transmission regime. This implies the possibility of designing quantum
systems that are invisible to tunneling by a passing wave packet.
