The presence of a deep-level trap coupled to a quantum-dot heterostructure is shown to provide a rapid energy-relaxation pathway through which electrons may thermalize. A capture process is considered whereby a free conduction-band electron is captured into the ground conduction-band state of a quantum dot by multiphonon-assisted tunneling through the trap. As an example calculation, transition rates for a 5 nm radius In0.5Ga0.5As/GaAs quantum dot coupled to the defect M1 are calculated as a function of separation between the quantum dot and the deep level. For separations less than 10 nm these rates are found to be in excess of 1010 s-1 at 4.2 K. The result suggests that the presence of point defects may serve to enhance the luminescence efficiency of quantum-dot material. The physical situation described in this paper could only arise if the spatial distribution of defects were strongly correlated with that of the quantum-dot structures, e.g., through formation of interface states or point defects as a consequence of the growth process. With this caveat, the proposed mechanism may possibly explain the failure to observe a significant phonon bottleneck effect in recent work on In1-xGaxAs quantum-dot structures [e.g., Appl. Phys. Lett. 64, 2815 (1994)]. © 1995 The American Physical Society.