Micellization of diblock copolymers with one long and weakly charged and one short uncharged block in an aqueous solution is considered on the basis of a lattice mean-field theory, The critical micellization concentration (cmc) is examined at different fractional charge and length of:the hydrophilic block as well as at different solvent quality and salt concentration. Above the cmc, the concentration of free copolymers and the micellar aggregation number are nearly constant. Volume fraction profiles show that the core-corona interface is sharp and that the hydrophilic segments are highly diluted in the corona. The dependences of the micellar aggregation number, the core radius, and corona thickness on several parameters are presented, and they agree qualitatively with scaling predictions. The predictions of the scaling relations are however restricted by the fact of limited scope of micellar stability when a single parameter is varied.