  We consider the convex subset $[A,B]$ of all elements between two levels $A$
and $B$ of a finite distributive lattice, as a union of (or covered by)
intervals $[a,b]$. A 1988 result of Voigt and Wegener shows that for such
convex subsets of finite Boolean lattices, covers using $\max(|A|,|B|)$
intervals (the minimum possible number) exist. In 1992 Bouchemakh and Engel
pointed out that this result holds more generally for finite products of finite
chains. In this paper we show that covers of size $\max(|A|,|B|)$ exist for
$[A,B]$ when $A$ is the set of atoms and $B$ the set of coatoms of any finite
distributive lattice. This is a consequence of a more general result for finite
partially ordered sets. We also speculate on the situation when other levels of
finite distributive lattices are considered, and prove a couple of theorems
supporting these speculations.
