There are two critical observations in multi-domain dialogue state tracking (DST) ignored in most existing work. First, the number of triples (domain-slot-value) in dialogue states generally increases with the growth of dialogue turns. Second, although dialogue states are accumulating, the difference between two adjacent turns is steadily minor. To model the two observations, we propose to divide the task into two successive procedures: progressive domain-slot tracking and shrunk value prediction. Specifically, domain-slot pairs are first modeled in a multi-level structure that can be predicted progressively based on previous turns. Then, we employ a generative approach to producing dialogue values for the predicted, rather than for all possible, domain-slot pairs. This divide-and-conquer approach not only enables parallelization for predicting domain-slot pairs, but also significantly reduces the number of domain-slot candidates for value prediction. Experimental results on the MultiWOZ datasets confirm that our methodology (PRO-DST) achieves very favorable improvement over existing methods.