We link micellar structures to their rheological properties for two surfactant body-wash formulations at various concentrations of salts and perfume raw materials (PRMs) using molecular simulations and micellar-scale modeling, as well as traditional surfactant packing arguments. The two body washes, namely, BW-1EO and BW-3EO, are composed of sodium lauryl- ethylene glycol ether sulfate (SLEnS, where rt is the average number of ethylene glycol repeat units), cocamidopropyl betaine (CAPB), ACCORD (which is a mixture of six PRMs), and NaCl salt. BW-3EO is an SLE3S-based body wash, whereas BW-1EO is an SLE1S-based body wash. Additional PRMs are also added into the body washes. The effects of temperature, salt, and added PRMs on micellar lengths, breakage times, end-cap free energies, and other properties are obtained from fits of the rheological data to predictions of the "Pointer Algorithm" [Zou, W.; Larson, R.G. J. Rheol. 2014, 58, 1-41], which is a simulation method based on the Cates model of micellar dynamics. Changes in these micellar properties are interpreted using the Israelachvili surfactant packing argument. From coarse-grained molecular simulations, we infer how salt modifies the micellar properties by changing the packing between the surfactant head groups, with the micellar- radius remaining nearly constant. PRMs do so by partitioning to different locations within the micelles according to their octanol/water partition coefficient Pow and chemical structures, adjusting the packing of the head and/or tail groups, and by changing the micelle radius, in the case of a large hydrophobic PRM. We find that relatively hydrophilic PRMs with log Pow < 2 partition primarily to the head group region and shrink micellar length, decreasing viscosity substantially, whereas more hydrophobic PRMs, with log Pow between 2 and 4, mix with the hydrophobic surfactant tails within the micellar core and slightly enhance the viscosity and micelle length, which is consistent with the packing argument. Large and very hydrophobic PRMs, with log Pow > 4, are isolated deep inside the micelle, separating from the tails and swelling the radius of the micelle, leading to shorter micelles and much lower viscosities, leading eventually to swollen-droplet micelles.