Development of light-emitting diodes (LEDs) based on colloidal quantum dots is driven by attractive properties of these fluorophores such as spectrally narrow, tunable emission and facile processibility via solution-based methods. A current obstacle towards improved LED performance is an incomplete understanding of the roles of extrinsic factors, such as non-radiative recombination at surface defects, versus intrinsic processes, such as multicarrier Auger recombination or electron-hole separation due to applied electric field. Here we address this problem with studies that correlate the excited state dynamics of structurally engineered quantum dots with their emissive performance within LEDs. We find that because of significant charging of quantum dots with extra electrons, Auger recombination greatly impacts both LED efficiency and the onset of efficiency roll-off at high currents. Further, we demonstrate two specific approaches for mitigating this problem using heterostructured quantum dots, either by suppressing Auger decay through the introduction of an intermediate alloyed layer, or by using an additional shell that impedes electron transfer into the quantum dot to help balance electron and hole injection.