The carrier density dependence of gain, index, and carrier lifetime has been measured for (InAs)1/(GaAs)4 short-period superlattice lasers. The 500-mu-m-long lasers have a threshold current density of 200 A/cm2 and exhibit a small carrier-induced change in refractive index (DELTA-n/DELTA-N approximately 2x10(-22) cm3). The small DELTA-n/DELTA-N also results in small linewidth enhancement factor (alpha approximately 1.1) of these lasers. The measured dependence of carrier lifetime on carrier density can be fitted to a bimolecular recombination model which suggests that radiative recombination is the dominant recombination mechanism in these structures.