Spin Hall nano-oscillators (SHNOs) are an emerging class of pure spin current driven microwave signal generators. Through the fabrication of 20 nm nano-constrictions in Pt/NiFe bilayers, we demonstrate that SHNOs can be scaled down to truly nanoscopic dimensions, with the added benefit of ultra-low operating currents and improved power conversion efficiency. The lateral confinement leads to a strong shape anisotropy field as well as an additional demagnetizing field whose reduction with increasing auto-oscillation amplitude can yield a positive current tunability contrary to the negative tunability commonly observed for localized excitations in extended magnetic layers. Micromagnetic simulations corroborate the experimental findings and suggest that the active magnetodynamic area resides up to 100 nm outside of the nano-constriction.