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Querying a relational database is difficult because it requires users to know both the SQL language and be familiar with the schema. On the other hand, many users possess enough domain familiarity or expertise to describe their desired queries by alternative means. For such users, two major alternatives to writing SQL are natural language interfaces (NLIs) and programming-by-example (PBE). Both of these alternatives face certain pitfalls: natural language queries (NLQs) are often ambiguous, even for human interpreters, while current PBE approaches require either low-complexity queries, user schema knowledge, exact example tuples from the user, or a closed-world assumption to be tractable. Consequently, we propose dual-specification query synthesis, which consumes both a NLQ and an optional PBE-like table sketch query that enables users to express varied levels of domain-specific knowledge. We introduce the novel dual-specification Duoquest system, which leverages guided partial query enumeration to efficiently explore the space of possible queries. We present results from user studies in which Duoquest demonstrates a 62.5% absolute increase in query construction accuracy over a state-of-the-art NLI and comparable accuracy to a PBE system on a more limited workload supported by the PBE system. In a simulation study on the prominent Spider benchmark, Duoquest demonstrates a >2x increase in top-1 accuracy over both NLI and PBE.