A new adiabatic pulse for population inversion and the principles of its design are presented. The pulse shape is characterized by the combination of two constraints. (i) Adiabatic following of the central isochromat of the spectral region of interest occurs with constant, possibly small adiabaticity parameter; thereby, the center isochromat gets most efficiently inverted. (ii) Frequency and amplitude modulations obey the principle of offset-independent adiabaticity; thus, the inversion dynamics of the center isochromat is extended over the desired bandwidth. Selective population inversion can be achieved rather independently of spatial radio frequency field inhomogeneities and with significantly reduced peak RF amplitude in comparison with the well-known sech/tanh adiabatic pulse.