This paper investigates the problem of answering compositional factoid questions over knowledge bases (KB) under efficiency constraints. The method, called TIPI, (i) decomposes compositional questions, (ii) predicts answer types for individual sub-questions, (iii) reasons over the compatibility of joint types, and finally, (iv) formulates compositional SPARQL queries respecting type constraints. TIPI’s answer type predictor is trained using distant supervision, and exploits lexical, syntactic and embedding-based features to compute context- and hierarchy-aware candidate answer types for an input question. Experiments on a recent benchmark show that TIPI results in state-of-the-art performance under the real-world assumption that only a single SPARQL query can be executed over the KB, and substantial reduction in the number of queries in the more general case.