Using (semi-)grand canonical Monte Carlo simulations of a polyelectrolyte chain of length N where the charges are in contact with a reservoir of constant chemical potential mu given by the solution pH, we study the behaviour of annealed polyelectrolytes in a poor solvent. We focus on the conformational properties in the close-to-Theta-point regime tau < tau* similar toN(-1/5)upsilon(-3/5), which can be reached either by reducing electrostatic interaction strength upsilon = lambda(B)/b or by improving solvent quality, i.e., by reducing tau = (Theta - T)/Theta. We investigate the conformations with regard to parameters upsilon, tau, and mu and explore in which conditions pearl-necklace-like structures are stable. Most of the pearl-necklace parameters are found to obey the scaling relations predicted for quenched polyelectrolytes. However, similarly to the behaviour known for this class of polyelectrolytes, we obtain large fluctuations in pearl number and size. In agreement with theoretical predictions we find a nonuniform charge distribution between pearls and strings. For tau much less than 1 and moderate interaction strength we demonstrate that a cascade of pearl-necklace transitions can be initiated by changing mu, i.e., by tuning the solution pH.