  Let $D>3$, $D\equiv3\;(4)$ be a prime, and let $\mathcal{C}$ be an ideal
class in the field $\mathbb{Q}(\sqrt{-D})$. In this article, we give a new
proof that $p(D,\mathcal{C})$, the smallest norm of a split prime
$\mathfrak{p}\in\mathcal{C}$, satisfies $p(D,\mathcal{C})\ll D^L$ for some
absolute constant $L$. Our proof is sieve theoretic. In particular, this allows
us to avoid the use of log-free zero-density estimates (for class group
$L$-functions) and the repulsion properties of exceptional zeros, two crucial
inputs to previous proofs of this result.
