  Using probabilistic methods, we obtain grid-drawings of graphs without
crossings with low volume and small aspect ratio. We show that every
$D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2
n\log n)$. In particular, every graph of bounded maximum degree can be drawn in
a grid with volume $O(n \log n)$.
