We have used two-color time-resolved spectroscopy to measure the relaxation of electron spin polarizations in a bulk semiconductor. The circularly polarized pump beam induces a polarization either by direct excitation from the valence band, or by free-carrier (Drude) absorption when tuned to an energy below the band gap. We find that the spin relaxation time, measured with picosecond time resolution by resonant induced Faraday rotation in both cases, increases in the presence of photogenerated holes. In the case of the material chosen, n-InSb, the increase was from 14 to 38 ps.