Previous work has identified the importance of the lipophilic-fluorophilic block length ratio in predicting the morphology of linear lipophilic-hydrophilic-fluorophilic (hereafter referred to as BAC) micelle systems. Here, a generalized form of this structural parameter is developed that makes no assumption of BAC triblock co-polymer linearity, while still providing accurate predictions of the micelle morphology. The morphologies of BAC micelles formed by triblock co-polymers with or have similar features, with the only notable difference being an inversion of the lipophilic and fluorophilic regions. A destabilization of the single-core micelle structure occurs as approaches unity from either direction. Finally, the extent to which the micelle morphology depends on the polymer architecture instead of the composition alone is examined, with a decreased patchiness observed in BAC systems with very long block lengths. Through the modification of both the -value and the polymer architecture, the micelle morphology can be effectively tuned for use in immobilized catalysis and nanoreactor applications.