The optical excitation of semiconductor gain media introduces both gain and refractive index changes, commonly referred to as amplitude-phase coupling. Quantum-confined structures with an energetically well separated carrier reservoir usually exhibit a decreased amplitude-phase coupling compared to bulk materials. However, its magnitude and definition is still controversially discussed. We investigate the fundamental processes influencing the amplitude-phase coupling in semiconductor quantum-dot media using a coupled-carrier rate-equation model. We are able to analyze the dependence on the electronic structure and suggest routes towards an optimization of the dynamic phase response of the gain material.