The best option if you can in a crevasse rescue scenerio would be to use a runner and tie a "Clove Hitch", not a girth hitch (clove hitch eliminates the torsional forces on the ice axe or picket from the fallen climber) near the center of the dead man ice axe. obviously on an ice axe you may want to cheat the runner a bit closer to the head of the axe since that the head has more surface area and greater friction when dragged through snow, and the last thing you want is for it to start slipping or spinning out.
Secondly if you have a second anchor the ice axe works much better than a picket (because it has rounded edges) for keeping the rope from digging into the lip of the crevasse, so I usually would try to use a picket as deadman-anchor in a crevasse fall situation, unless tools were all I was carrying.