We report on a characterization of fundamental gain dynamics in recently developed InAs/InP quantum-dot semiconductor optical amplifiers. Multi-wavelength pump-probe measurements were used to determine gain recovery rates, following a powerful optical pump pulse, at various wavelengths for different bias levels and pump excitation powers. The recovery was dominated by coupling between the electronic states in the quantum-dots and the high energy carrier reservoir via capture and escape mechanisms. These processes determine also the wavelength dependencies of gain saturation depth and the asymptotic gain recovery level. Unlike quantum-dash amplifiers, these quantum-dots exhibit no instantaneous gain response, confirming their quasi zero-dimensional nature. © 2014 AIP Publishing LLC.