Matching Dependencies (MDs) are a recent proposal for declarative entity resolution. They are rules that specify, given the similarities satisfied by values in a database, what values should be considered duplicates, and have to be matched. On the basis of a chase-like procedure for MD enforcement, we can obtain clean (duplicate-free) instances; possibly several of them. The clean answers to queries (which we call the resolved answers) are invariant under the resulting class of instances. Identifying the clean versions of a given instance is generally an intractable problem. In this paper, we show that for a certain class of MDs, the characterization of the clean instances is straightforward. This is an important result, because it leads to tractable cases of resolved query answering. Further tractable cases are derived by making connections with tractable cases of CQA.