SUMMARYIn this letter, we propose a novel kind of uncertain query, top (k 1 , k 2 ) query. The x-tuple model and the possible world semantics are used to describe data objects in uncertain datasets. The top (k 1 , k 2 ) query is going to find k 2 x-tuples with largest probabilities to be the result of top k 1 query in a possible world. Firstly, we design a basic algorithm for top (k 1 , k 2 ) query based on dynamic programming. And then some pruning strategies are designed to improve its efficiency. An improved initialization method is proposed for further acceleration. Experiments in real and synthetic datasets prove the performance of our methods. key words: uncertain query, top k, x-tuple, possible world