A theoretical study is presented of the scattering by ionized impurities of conduction electrons in some III-V compounds. In particular, we consider a degenerate material whose conduction band possesses an absolute minimum at the center Γ of the Brillouin zone having a small effective mass and subsidiary minima near the points L. As the carrier concentration increases, the screening length decreases abruptly when the Fermi level reaches the bottom of the subsidiary minima. This effect is dominant despite the onset of intervalley scattering. Thus, the lifetime of the electrons in the central minimum exhibits a sharp increase when the secondary minima begin to fill up. This result accounts for the increase in amplitude of the Shubnikov-de Haas effect in GaSb with increasing carrier concentration.