  A radio labeling of a graph $G$ is a mapping $f: V(G) \rightarrow \{0, 1, 2,
\ldots\}$ such that $|f(u)-f(v)|\geq d + 1 - d(u,v)$ for every pair of distinct
vertices $u, v$ of $G$, where $d$ is the diameter of $G$ and $d(u,v)$ the
distance between $u$ and $v$ in $G$. The radio number of $G$ is the smallest
integer $k$ such that $G$ has a radio labeling $f$ with $\max\{f(v) : v \in
V(G)\} = k$. We give a necessary and sufficient condition for a lower bound on
the radio number of trees to be achieved, two other sufficient conditions for
the same bound to be achieved by a tree, and an upper bound on the radio number
of trees. Using these, we determine the radio number for three families of
trees.
