  The {\em independent domination number} $\gamma^i(G)$ of a graph $G$ is the
maximum, over all independent sets $I$, of the minimal number of vertices
needed to dominate $I$. It is known \cite{abz} that in chordal graphs
$\gamma^i$ is equal to $\gamma$, the ordinary domination number. The weighted
version of this result is not true, but we show that it does hold for interval
graphs, and for the intersection (that is, line) graphs of subtrees of a given
tree, where each subtree is a single edge.
