Before stacking, grasp the very tips of the cut hairs between thumb and index finger, purse your lips and blow hard into the base of the hairs (Sometimes a little 'rolling' action of the tips will aid the process).

Pinch the cut ends in your other hand and you will have nearly all of the "fines" and underfur ready to remove from the tip end. Just pull them through and dispose or save for a dubbing.