We investigate solute encapsulation by copolymer micelles by performing discontinuous molecular dynamics simulations on a model solute-copolymer- solvent system. In this paper, we detail the effect of system density, copolymer mole fraction, and hydrophobic interaction between copolymer head and solute on the encapsulation efficiency and phase behavior of the system. The relative hydrophobicity of solute and copolymer head units acts as a coupling parameter that determines whether the system encapsulates or the copolymer and solute aggregate separately. The presence of solute particles makes micelles form more easily than they would otherwise. Five different mesophases or morphologies are possible. The micelle-unimer transition that occurs in a solute-free copolymer-solvent system is, for moderately hydrophobic solute particles, replaced by a transition between a micelle phase and a morphology in which copolymers surround a large aggregate of solute particles. The best encapsulation occurs for highly hydrophobic solute particles where solutes are dispersed throughout the micelle's core. The manner in which our results might be used by experimentalists to improve the encapsulation behavior of drug-copolymer systems is discussed.