We demonstrate low-pump-power operation of a self-mode-locked Ti:sapphire laser. Stable, sub-20-fs duration pulses, with output powers of 35-100 mW, were obtained for pump powers in the range of 400 mW-1 W. Our design uses a tight focusing geometry for both the argon-ion and Ti:sapphire beams within the Ti:sapphire crystal, which significantly reduces the pump-power requirements.