We demonstrate experimentally that solid-state lasers with strong solitonlike pulse shaping can be mode locked by a slow saturable absorber only, i.e., the response time is much slower than the width of the soliton. A Ti:sapphire laser mode locked by a low-temperature-grown GaAs absorber with 10-ps recovery time generates pulses as short as 300 fs without the need for Kerr-lens mode locking and critical cavity alignment. An extrapolation of this result would predict that an ≈100-fs recovery time of a semiconductor absorber could support pulses into the 10-fs regime.