I will discuss a new class of potentials for pseudo Nambu-Goldstone bosons (pNGBs) arising from the spontaneous breaking of a non-Abelian SO(N) global symmetry. These potentials take the form of Gegenbauer polynomials and are radiatively stable. I will use them to build new pNGB Higgs scenarios, “Gegenbauer Higgs” and “Gegenbauer’s Twin”, that can significantly reduce the fine-tuning compared to previous constructions. In particular, the second model can realize fully natural electroweak symmetry breaking consistently with current LHC measurements, and predicts large corrections to the Higgs cubic coupling that may be observed at the High-Luminosity phase of the LHC.