Twisting the strands together well prior to forming the loop is the key. Twisting the wires counterclockwise helps lots.
As manufactured, the strands have a clockwise twist (if you imaging the wire coming out of the clock face
). Twist the strands the other way, prior to forming the loop. When the strands are twisted _clockwise_, than as the head of the screw pushes against them, the strands get pushed away from the screw shaft. When the strands are twisted _counterclockwise_, then has the screw head turns the strands get pushed toward the screw shaft.
But if the strands are well twisted together, you can terminate the wire neatly without the 'birds nest' of strands being pushed from under the screw head. The counterclockwise twist is more important with larger wire relative to the screw head size.
-Jon