This article deals with consistent query answering to conjunctive queries under primary key constraints. The repairs of an inconsistent database db are obtained by selecting a maximum number of tuples from db without ever selecting two tuples that agree on their primary key. For a Boolean conjunctive query q, we are interested in the following question: does there exist a Boolean first-order query such that for every database db, evaluates to true on db if and only if q evaluates to true on every repair of db? We address this problem for acyclic conjunctive queries in which no relation name occurs more than once. Our results improve previous solutions that are based on Fuxman-Miller join graphs. Categories and Subject Descriptors H.2.3 [Database Management]: Languages--query languages; H.2.4 [Database Management]: Systems--relational databases General Terms Theory, Algorithms Keywords Conjunctive queries, consistent query answering, database repairing, primary key, query rewriting