Aberration-corrected Z-contrast scanning transmission electron microscopy of core/shell nanocrystals shows clear correlations between structure and quantum efficiency. Uniform shell coverage is obtained only for a graded CdS/ZnS shell material and is found to be critical to achieving near 100% quantum yield. The sublattice sensitivity of the images confirms that preferential growth takes place on the anion-terminated surfaces. This explains the three-dimensional "nanobullet" shape observed in the case of core/shell nanorods.