The eccentricity of a vertex v of a connected graph G is the distance from v to a vertex farthest from v in G. The center of G is the subgraph of G induced by the vertices having minimum eccentricity. For a vertex v in a 2-edge-connected graph G, the edge-deleted eccentricity of v is defined to be the maximum eccentricity of v in G − e over all edges e of G. The edge-deleted center of G is the subgraph induced by those vertices of G having minimum edge-deleted eccentricity. The edge-deleted central appendage number of a graph G is the minimum difference |V (H)| − |V (G)| over all graphs H where the edgedeleted center of H is isomorphic to G. In this paper, we determine the edge-deleted central appendage number of all trees.