When small concentrations of A-b-B diblock copolymer are mixed with selective solvent or A homopolymer, they often form spherical micelles with cores comprised of the B blocks. Mean field theory predicts that the core radii scale primarily with the degree of polymerization of the B block as Z(CB)(alpha) with alpha similar or equal to 2/3 or larger, and this is consistent with many experimental data. However, recent experiments on very strongly segregated "crew-cut" micelles indicate a much weaker dependence. In this paper, we study crew-cut micelles using a simple mean field theory and Monte Carlo simulations. The Monte Carlo simulations include the calculation of the system relaxation times, which are used both to determine the simulation times required to reach equilibrium and to examine, at least qualitatively, the variable solvent qualities at which the micelle structures become "frozen in" for different polymer molecular weights. The mean field results for these crew-cut, strongly segregated micelles are consistent with previous mean field calculations, giving alpha = 0.77 at fixed solvent quality. The Monte Carlo results indicate that nonequilibrium effects result in a weaker power law, as observed experimentally.