  A graph is called set-sequential if its vertices can be labeled with distinct
nonzero vectors in $\mathbb{F}_2^n$ such that when each edge is labeled with
the sum$\pmod{2}$ of its vertices, every nonzero vector in $\mathbb{F}_2^n$ is
the label for either a single vertex or a single edge. We resolve certain cases
of a conjecture of Balister, Gyori, and Schelp in order to show many new
classes of trees to be set-sequential. We show that all caterpillars $T$ of
diameter $k$ such that $k \leq 18$ or $|V(T)| \geq 2^{k-1}$ are set-sequential,
where $T$ has only odd-degree vertices and $|T| = 2^{n-1}$ for some positive
integer $n$. We also present a new method of recursively constructing
set-sequential trees.
