The recovery time of absorption in semiconductor quantum-well structures is one of the key parameters that determines the performance of pulsed lasers mode-locked or Q-switched by semiconductor saturable absorbers. In this paper we discuss new methods to control the recovery time of absorption. The first method is based on controlling the crystalline quality of the absorbing material and thus the density of non-radiative recombination centers that are responsible for the fast recovery of the absorption. With this technique, we were able to fabricate semiconductor saturable absorber mirrors (SESAMs) with recovery times of about 4.5 ps at 1 mu m and 40 ps at 1.55 mu m. Another approach that we propose and demonstrate in this paper is based on band-gap engineering that enables short recovery times to be achieved through fast relaxation of excited photocarriers via intraband scattering. A 24 ps carrier decay time was achieved by placing deep quantum-wells next to the shallow quantum-wells responsible for the nonlinear absorption. We demonstrated that the recovery time can be changed by modifying the thickness of the deep and shallow quantum-wells.