Summary: The parameter \(t\) of a tree \(t\)-spanner of a graph is always bounded by \(2\lambda\) where \(\lambda\) is the diameter of the graph. In this paper we establish a sufficient condition for graphs to have the minimum spanner at least \(2\rho-1\) where \(\rho\) is the radius. We also obtain a characterization for tree 3-spanner admissible chordal graphs in terms of tree 3-spanner admissibility of certain subgraphs.