The effect of solvent selectivity on the fragmentation kinetics of spherical micelles formed by a 1,2-polybutadiene-block-poly(ethylene oxide) "BO" copolymer in five 1-alkyl-3-methylimidazolium bis (trifluoromethylsulfonyl)imide-based ionic liquids (ILs), ([CnMIM] [TFSI], where n = methyl, ethyl, butyl, hexyl, and octyl) was investigated by temperature-jump dynamic light scattering (T-jump DLS), small-angle X-ray scattering (SAXS), and liquid-phase transmission electron microscopy (LP-TEM). In this system, the core-forming block is 1,2-polybutadiene and the corona-forming block is poly (ethylene oxide). Micelle solutions prepared by direct dissolution of the polymer into the IL resulted in large, polydisperse spherical aggregates. For these micelles, with aggregation numbers far from equilibrium, it was found that fragmentation is the most favorable equilibration mechanism; previous measurements demonstrated that no single chain exchange occurs under these conditions. T-jump DLS showed that the decay of R-h during annealing at 170 degrees C is, surprisingly, almost independent of the IL selectivity. This observation was confirmed by SAXS and LP-TEM, where the decay of R-core during annealing at 170 degrees C was found to occur on the same timescale regardless of the solvent quality. For all relaxation techniques used, and in all the ILs studied, the decay in micelle size could be well fit to the Avrami equation or "compressed exponential" with an exponent (n) of 2, except for the decay in R-h in the most selective IL. Based on the change in the aggregation number, Q before and after a T-jump to 170 degrees C, the selectivity of the IL determines how far the initial micelles are from equilibrium, but the fragmentation proceeds on the order of hundreds of minutes in all cases. SAXS of the bulk block copolymer revealed a lamellar morphology with a domain size of the core-forming block of 21 nm, which is comparable to the initial core radius of micelles prepared by direct dissolution, but well above the resulting core radii after fragmentation. We discuss possible explanations for the functional form of the relaxation function, and the apparent independence of the rate on interfacial tension.