The need for efficient and effective data exploration has resulted in several solutions that automatically recommend interesting visualizations. The main idea underlying those solutions is to automatically generate all possible views of data, and recommend the top-k interesting views. However, those solutions assume that the analyst is able to formulate a well-defined query that selects a subset of data, which contains insights. Meanwhile, in reality, it is typically a challenging task to pose an exploratory query, which can immediately reveal some insights. To address that challenge, in this work we propose utilizing query refinement as one technique that allows to automatically adjust the analyst's input query to discover such valuable insights. However, a naive query refinement, in addition to generating a prohibitively large search space, also raises other problems such as deviating from the user's preference and recommending statistically insignificant views. In this paper, we address those problems and propose a novel suit of schemes, which efficiently navigate the refined queries search space to recommend the top-k insights that meet all of the analyst's pre-specified criteria.