The behavior of a fenofibrate aggregate in water and its interaction with pure sodium taurodeoxycholate (TDC) micelles, as well as with mixed micelles of TDC and fatty acids (myristic, oleic, and stearic), was studied using atomistic molecular dynamics simulations. For each system, 500 ns trajectories were generated and analyzed in terms of the association of amphiphiles around the drug aggregate and their impact on the morphology and intermolecular interactions of the drug molecules. The results show that in the absence of fatty acids TDC covers the surface of the drug aggregate, shielding it from water without disrupting its structure. In contrast, all studied fatty acids intercalate between the drug molecules in the aggregate. However, myristic and stearic acids do not shield sufficiently the drug molecules from water, while oleic acid significantly reduces the contact between water and drug molecules. Two key requirements for effective solubilization are identified: (1) the ability of amphiphiles to disrupt the nanostructure of the drug aggregate, and (2) the flexibility and capability of amphiphiles to reduce interactions between water and hydrophobic drug molecules. These requirements were used to evaluate the efficiency of fatty acids in increasing the solubilization capacity of TDC micelles. A very good correlation was established between the efficiency determined from molecular dynamics simulations and experimental data known from the literature. The methodology developed in this study could be widely used to compare the efficiency of new lipid-based drug delivery formulations to solubilize hydrophobic drug molecules.