In this Letter, a theoretical analysis shows that for complete population inversion, the adiabatic population inversion due to chirp (APIC) has much the same time evolution as adiabatic inversion. We show that APIC is caused by a long frequency sweep in place of an infinitesimal interaction, and is more important than the positive chirp effect. We also show that arbitrary pulse durations can be selected if a suitable Rabi frequency, i.e., the laser intensity, and chirp rate are chosen. This conclusion means that APIC is a very effective method in the case when a system has ultrafast relaxation. (C) 2002 Elsevier Science B.V. All rights reserved.