Solubilization of relatively hydrophobic organic compounds (solubilizates) by the core of poly(methyl methacrylate)-block-poly(acrylic acid) (PMMA-PAAc) micelles in D2O was theoretically simulated and experimentally studied for a number of compounds such as chloroform, chlorobenzene, 4-methylcyclohexanone, benzene, toluene, cyclohexane, and hexane. The experimental results show that (i) the core-captured amount of the solubilizate as well as its solubilization rate chiefly depend on its interaction with PMMA (expressed, e.g., by its X-parameter), (ii) the limiting solubilization degree may also be determined by other thermodynamic factors, in particular the core-water interphase tension, (iii) the solubilization rate and partly the equilibrium solubilization degree are also influenced by shell-core interactions, (iv) most solubilizates, except chloroform, swell the core with a surprisingly narrow front, which could indicate a steep concentration dependence of their diffusion coefficient but also (v) there is morphological inhomogeneity of the core with more easily accessible domains in the outer part of the core. The last conclusion is also supported by the much lower solubilization rates observed with micelles formed by copolymers with longer PMMA blocks.