Let $S$ be a set of $n$ points in the unit square $[0,1]^2$, one of which is
the origin. We construct $n$ pairwise interior-disjoint axis-aligned empty
rectangles such that the lower left corner of each rectangle is a point in $S$,
and the rectangles jointly cover at least a positive constant area (about
0.09). This is a first step towards the solution of a longstanding conjecture
that the rectangles in such a packing can jointly cover an area of at least
1/2.