  Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove
the following result. Let $R$ be a commutative Noetherian ring and $a$ an ideal
in the Jacobson radical of $R$. Let $\hat{R}^a$ be the $a$-adic completion of
$R$. If $M$ is a finitely generated $R$-module such that
$\ext^i_R(\hat{R}^a,M)=0$ for all $i\neq 0$, then $M$ is $a$-adically complete.
