Thermodynamic vs kinetic aspects of the formation of crew-cut aggregates of various structures prepared from polystyrene-b-poly(acrylic acid) diblock copolymers in DMF/water mixtures are explored. In particular, the reversibility of the transitions between the crew-cut aggregates of various morphologies is studied by "jumps" in the polymer or ion concentration at various water contents. The aggregates are prepared by two different methods: micellization is induced either by the addition of water to polymer/DMF solutions or by the direct dissolution of the polymer in DMF/water mixtures. It is shown that as the polymer concentration increases, the morphology of the aggregates changes from spheres to rodlike micelles, to interconnected rods, and then to bilayers. As the water content increases, the boundaries for the formation of the different morphologies move toward lower polymer concentrations. The thermodynamic vs kinetic control of the morphology depends largely on the water content and the method of aggregate formation. When water content is lower than 6.5 wt %, the formation of the aggregates is controlled by thermodynamics of micellization, and the morphological transitions are reversible. When the water content is between 7.5 and 9.5%, the morphology of the aggregates depends on the method of aggregate preparation. In this range of water contents, the morphological reversibility decreases significantly; for example, transitions from spheres to rods and then to bilayers are not achievable kinetically within a period of several days. The slow kinetics for the morphological transitions are mainly due to a low rate of polymer chain exchange and the strong repulsive interactions among the aggregates. The kinetics can be accelerated by decreasing the strength of the repulsive interactions and increasing the efficiency of adhesive collisions between the micelles through addition of ions or of polymer. Two different mechanisms for the morphological transitions as well as their kinetic aspects are discussed.