We performed theoretical and experimental investigations of dilute solutions of micelles of neutral amorphous diblock copolymers in selective solvents. The ranges of thermodynamic stability of spherical, cylindrical, and lamellar morphologies along with the equilibrium sizes and aggregation numbers of micelles are calculated and measured. For high molecular weight copolymers it is shown that the sphere-to-cylinder transition as well as precipitation of the micelles associated with cylinder-to-lamella transition occurs when aggregates have a crew-cut structure with the thickness of the corona smaller than the radius of the core, Similar to starlike micelles with corona larger than the core, the equilibrium parameters of crew-cut micelles are determined by the balance between the free energy of the corona and the surface energy of the core. The elastic free energy of the core remains small compared to the corona and surface free energies; however, it determines the transitions between different morphologies. The theoretical predictions including the existence of crew-cut spherical micelles, the range of stability of cylindrical micelles, and the significance of the contributions of the logarithmic corrections to scaling are in good agreement with experiments on polystyrene-polyisoprene block copolymer micelles in heptane, a selective solvent for the polyisoprene block.