We have made direct pump-probe measurements of spin lifetimes in intrinsic and degenerate n-InAs at 300 K. In particular, we measure remarkably long spin lifetimes (tau(s)similar to1.6 ns) for near-degenerate epilayers of n-InAs. For intrinsic material, we determine tau(s)similar to20 ps, in agreement with other workers. There are two main models that have been invoked for describing spin relaxation in narrow-gap semiconductors: the D'yakonov-Perel (DP) model and the Elliott-Yafet (EY) model. For intrinsic material, the DP model is believed to dominate in III-V materials above 77 K, in agreement with our results. We show that in the presence of strong n-type doping, the DP relaxation is suppressed both by the degeneracy condition and by electron-electron scattering, and that the EY model then dominates for the n-type material. We show that this same process is also responsible for a hitherto unexplained lengthening of tau(s) with n-type doping in our earlier measurements of n-InSb.