We report photoluminescence, linear absorption and femto-second transient bleaching spectra for a colloidal solution of indium phosphide (InP) quantum dots at ambient temperatures. The photoluminescence quantum yield is shown to depend not only upon the size of the quantum dots, with larger dots exhibiting higher quantum yields, but also upon the excitation wavelength. At short wavelengths, photoluminescence excitation spectra deviate markedly from the absorption spectra indicating that an efficient non-radiative deactivation pathway becomes prominent at these higher photon energies. We interpret this observation in terms of an inefficient relaxation mechanism between the second excited state and the lowest energy excited state from which the emission emanates. The results are consistent with the existence of a phonon bottleneck.