Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s --> 5p --> 5d of the rubidium atom by frequency-swept ultrashort laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s --> 5p transition, and later with the 5p --> 5d transition. With this "intuitive" scheme it is possible to achieve complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a "counterintuitive" direction of the frequency sweep, in which case population of the intermediate level during the pulse is strongly reduced.