The systematics of experimental energy differences between the levels of the ground state band and the gamma-1 band in even-even nuclei are studied as a function of the angular momentum L, demonstrating a decrease of the energy differences with increasing L, in contrast to what is seen in vibrational, gamma-unstable, and triaxial nuclei. After a short review of the relevant predictions of several simple collective models, it is shown that this decrease is caused in the framework of the proxy-SU(3) scheme by the same three-body and/or four body operators which break the degeneracy between the ground state band and the gamma-1 band, predicting in parallel the correct form of odd-even staggering within the gamma-1 bands.
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