  Let $\text{ch}(G)$ denote the choice number of a graph $G$ (also called "list
chromatic number" or "choosability" of $G$). Noel, Reed, and Wu proved the
conjecture of Ohba that $\text{ch}(G)=\chi(G)$ when $|V(G)|\le 2\chi(G)+1$. We
extend this to a general upper bound: $\text{ch}(G)\le
\max\{\chi(G),\lceil({|V(G)|+\chi(G)-1})/{3}\rceil\}$. Our result is sharp for
$|V(G)|\le 3\chi(G)$ using Ohba's examples, and it improves the best-known
upper bound for $\text{ch}(K_{4,\dots,4})$.
