A paired-dominating set of a graph \(G\) is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of \(G\) is the minimum cardinality of a paired-dominating set of \(G\), and is obviously bounded below by the domination number of \(G\). We give a constructive characterization of the trees with equal domination and paired-domination numbers.