Optical-confinement-factor GAMMA-dependencies of the K factor, differential gain dg / dN, and nonlinear gain coefficient epsilon, for 1.55-mu-m InGaAs/InGaAsP multiple-quantum-well (MQW) and compressively strained MQW lasers, were investigated experimentally. For both MQW and strained-MQW lasers, when GAMMA-is increased, the K factor is reduced, dg / dN is increased but epsilon-is almost constant. These results indicate that the GAMMA-dependence of the K factor mainly results from a change in dg / dN, and does not result from a change in epsilon. For the strained MQW lasers, the K factor, dg / dN and epsilon are, respectively, half as large, twice as large and the same as those for the MQW lasers, when both types of lasers have the same GAMMA-(= 0.05). This suggests that the strained MQW lasers with a large GAMMA-are expected to have a small K factor and thus be preferable in achieving large modulation bandwidths.