A theory describing the self-assembly of diblock copolymers with a weak (annealing) polyelectrolyte block and a hydrophobic block is developed. Copolymers with short hydrophobic and long polyelectrolyte block form starlike micelles in aqueous solution; otherwise, crew-cut micelles are found. We demonstrate that there is strong coupling between copolymer self-assembly and ionization of the polyelectrolyte block. At low pH and/or low salt concentration large quasi-neutral micelles with nondissociated coronae are stable. An increase in salt concentration promotes ionization of coronae and leads to the decrease in aggregation number. The structural rearrangement occurs continuously for crew-cut micelles while for starlike micelles the jump-wise morphological transition is predicted. A subsequent increase in salt concentration results in increasing aggregation number accompanied by weak decrease in the corona span. An increase in pH leads to,decreasing aggregation number and increasing span of the corona; this rearrangements occur continuously or (in the case of starlike micelles) discontinuously. The phase diagrams of the micellar solution in salt concentration-pH coordinates are obtained. The exponents for the corresponding power law dependences and cmc are calculated in the mean-field approximation.