Anisotropic shape and band structure engineered into double-heterojunction nanorods (DHNRs) can improve and impart new optical/optoelectronic capabilities in colloidal quantum dot-based devices. However, the photoluminescence quantum yield of DHNRs, which is significantly lower than the near-ideal limit recently achieved in the state-of-the-art core/shell quantum dots, remains as their main limitation. Here, we examine how the photoluminescence of CdS/CdSe/ZnSe DHNRs is affected by (1) the length of the CdS seed nanorods, (2) the rod and tip diameter dependent variations in band offset, and (3) the CdSe-like islands on the sides of DHNRs that can result as a side-product of ZnSe shell growth. By understanding and optimizing these three key parameters, we demonstrate an improvement in the photoluminescence quantum yield up to 93% (up to 62% for excitation above CdS bandgap) while retaining useful shape anisotropy and the band structure design in DHNRs.