  The degree set of a finite simple graph $G$ is the set of distinct degrees of
vertices of $G$. A theorem of Kapoor, Polimeni & Wall asserts that the least
order of a graph with a given degree set $\mathscr D$ is $1+\max \mathscr D$.
Tripathi & Vijay considered the analogous problem concerning the least size of
graphs with degree set $\mathscr D$. We expand on their results, and determine
the least size of graphs with degree set $\mathscr D$ when (i) $\min \mathscr D
\mid d$ for each $d \in \mathscr D$; (ii) $\min \mathscr D=2$; (iii) $\mathscr
D=\{m,m+1,\ldots,n\}$. In addition, given any $\mathscr D$, we produce a graph
$G$ whose size is within $\min \mathscr D$ of the optimal size, giving a
$\big(1+\frac{2}{d_1+1})$-approximation, where $d_1=\max \mathscr D$.
