Many theoretical studies and some experiments have shown the possibility of several new secondary quantum effects in small Josephson junctions at low temperatures. We show that, within the well-established quantum picture of the junction, it is possible to experimentally observe sharp voltalge peaks at certain current values. Such peaks are related to a resonant macroscopic quantum tunneling between levels in neighboring wells of the proper washboard potential having close energies. The proposed experiment, with respect to experiments on Coulomb blockade or Block oscillations, requires a larger junction area, reducing the technological difficulties in making the samples.