Designing a versatile nanocarrier platform that can be tailored to deliver specific drug payloads is challenging. In general, effective drug encapsulation, high drug-loading capacity, uniform shape and size distribution, and enhanced stability are among the fundamental attributes of a successful nanocarrier design. These physiochemical features of the nanocarriers are intimately tied to the specific drug payload that they are tasked to deliver. The molecular architecture of the nanocarrier's scaffold often needs to be tuned for each drug, especially if the target drugs are structurally and chemically distinct as in the case of doxorubicin (DOX) and paclitaxel (PTX). Starting from our previously reported telodendrimeric block copolymer platform optimized for PTX, we analyze three generations of telodendrimer architectures to arrive at the design that is capable of encapsulating another important chemotherapeutic drug, DOX. Multiple long-time-scale self-assembly simulations were performed both in atomistic and coarse-grained resolutions to generate equilibrated DOX-encapsulated nanocarriers. The results show how subtle changes in the molecular architecture of the telodendrimer head groups have profound effects on the nanocarrier size, morphology, and asphericity. The simulation results are in agreement with the experimental data for DOX-encapsulated nanocarriers. This work emphasizes the increasing role of molecular simulations in the rational design of nanocarriers, thereby eliminating the trial and error method that has been prevalent in experimental synthesis. The molecular-level insights gained from the simulations will be used to design the next generation of drug-specific nanocarriers.