Evidence is presented to show that a group of nuclei, spanning a range of structures, corresponds to a previously proposed isolated region of regular behavior between vibrational and rotational structures that was never before observed empirically. Nuclei predicted to show such regular spectra correspond to Hamiltonian parameters that lie amidst those giving more chaotic spectra. We identify a key observable that has a one-to-one correspondence to this arc of regularity and which therefore provides both an empirical signature for it and a clue to its underlying nature.