Carrier transfer into quantum dots has been investigated by time-resolved photoluminescence spectroscopy in a set of In0.6Ga0.4As/GaAs quantum dot structures with gradually changing interband transition and intraband level energies. Quantum dot energy levels were tuned by thermal compositional disordering of the inter-face. Time-resolved photoluminescence for low photoexcited carrier densities show efficient electron relaxation by LO phonon emission for samples in which the electron energy level separation is close to the LO phonon energy. Slower carrier transfer in samples with abrupt quantum dot/barrier interfaces is also found, the latter is attributed to strain-induced or compositional potential barriers at the quantum dot inter-face.