Probabilistic databases hold promise of being a viable means for large-scale uncertainty management, increasingly needed in a number of real world applications domains. However, query evaluation in probabilistic databases remains a computational challenge. Prior work on efficient exact query evaluation in probabilistic databases has largely concentrated on query-centric formulations (e.g., safe plans, hierarchical queries), in that, they only consider characteristics of the query and not the data in the database. It is easy to construct examples where a supposedly hard query run on an appropriate database gives rise to a tractable query evaluation problem. In this paper, we develop efficient query evaluation techniques that leverage characteristics of both the query and the data in the database. We focus on tuple-independent databases where the query evaluation problem is equivalent to computing marginal probabilities of Boolean formulas associated with the result tuples. Query eval...