  A configuration of a graph is an assignment of one of two states, on or off,
to each vertex of it. A regular move at a vertex changes the states of the
neighbors of that vertex. A valid move is a regular move at an on vertex. The
following result is proved in this note: given any starting configuration $x$
of a tree, if there is a sequence of regular moves which brings $x$ to another
configuration in which there are $\ell$ on vertices then there must exist a
sequence of valid moves which takes $x$ to a configuration with at most $\ell
+2$ on vertices. We provide example to show that the upper bound $\ell +2$ is
sharp. Some relevant results and conjectures are also reported.
