  A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two
incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt
proved that any two maximal CD-independent subsets of a finite distributive
lattice have the same number of elements. In this paper, we prove that if $L$
is a finite meet-distributive lattice, then the size of every CD-independent
subset of $L$ is at most the number of atoms of $L$ plus the length of $L$. If,
in addition, there is no three-element antichain of meet-irreducible elements,
then we give a recursive description of maximal CD-independent subsets.
Finally, to give an application of CD-independent subsets, we give a new
approach to count islands on a rectangular board.
