  We observe message-efficient distributed algorithms for the Set Cover
problem. Given a ground set $U$ of $n$ elements and $m$ subsets of $U$, we aim
to find the minimal number of these subsets that contain all elements. In the
default distributed setup of this problem, each set has a bidirected
communication link with each element it contains. Our first result is a
$\tilde{O}(\log^2(\Delta))$-time and $O(\sqrt{\Delta)}(n+m))$-message algorithm
with expected approximation ration of $O(\log(\Delta))$ in the $KT_0$ model.
The value $\Delta$ denotes the maximal cardinality of each subset. Our
algorithm is \emph{almost} optimal with regard to time and message complexity.
Further, we present Set Cover algorithm in the Beeping model that only relies
on carrier-sensing and can trade runtime for approximation ratio similar to the
celebrated algorithm by Kuhn and Wattenhofer [PODC '03].
