  The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values
of the eigenvalues of $G$. An $n$-vertex graph is said to be hypoenergetic if
$E(G)<n$ and strongly hypoenergetic if $E(G)<n-1$. In this paper, we consider
hypoenergetic and strongly hypoenergetic trees. For any given $n$ and $\Delta$,
the existence of both hypoenergetic and strongly hypoenergetic trees of order
$n$ and maximum degree $\Delta$ is completely characterized.
