  Enochs' conjecture asserts that each covering class of modules (over any
fixed ring) has to be closed under direct limits. Although various special
cases of the conjecture have been verified, the conjecture remains open in its
full generality. In this short paper, we prove the validity of the conjecture
for small precovering classes, i.e. the classes of the form $\mathrm{Add}(M)$
where $M$ is any module, under a mild additional set-theoretic assumption which
ensures that there are enough non-reflecting stationary sets. We even show that
$M$ has a perfect decomposition if $\mathrm{Add}(M)$ is a covering class.
Finally, the additional set-theoretic assumption is shown to be redundant if
there exists an $n<\omega$ such that $M$ decomposes into a direct sum of
$\aleph_n$-generated modules.
