Answering complex questions over knowledge bases (KB-QA) faces huge input data with billions of facts, involving millions of entities and thousands of predicates. For efficiency, QA systems first reduce the answer search space by identifying a set of facts that is likely to contain all answers and relevant cues. The most common technique or doing this is to apply named entity disambiguation (NED) systems to the question, and retrieve KB facts for the disambiguated entities. This work presents CLOCQ, an efficient method that prunes irrelevant parts of the search space using KB-aware signals. CLOCQ uses a top-k query processor over score-ordered lists of KB items that combine signals about lexical matching, relevance to the question, coherence among candidate items, and connectivity in the KB graph. Experiments with two recent QA benchmarks for complex questions demonstrate the superiority of CLOCQ over state-of-the-art baselines with respect to answer presence, size of the search space, and runtimes