Law Review Write-On Competitions, from a Law Review Editor:

I'm not sure how representative these views are, and I can see a downside to following this advice. But my correspondent has fresher experience with grading papers than I have, so I thought the advice would be worth passing along:

You mention in the book already [my correspondent is talking about my Academic Legal Writing book] that if you think of more than one possible thesis, you should choose the more creative one. I think this is much more important than you make it seem. This year, our competition was about [a topic that implicated a circuit split].... Out of my alloted stack of 22 papers, about 18 of them took one side or the other (or some more complicated position) on the circuit split.

The other 4 papers had very different sorts of theses.... All of these topics [that the 4 papers focused on] were mentioned in the cases and supplementary materials, and there were enough sources to make a 7-page comment out of it, but the topics were not clearly indicated by the packet materials.

These papers were at a significant advantage. First, they got all the creativity points instantaneously, though for us this was only 2 points out of 45 total. More importantly, they put the grader in a good mood after the monotony of reading the same thesis elaborated over and over. And even more importantly, I hadn't been primed with the counterarguments already, so the papers probably got more points for thoroughness and convincingness of arguments than they would have if I'd seen 20 papers making various counterarguments.

I should note also that I followed this "ignore the circuit split" strategy when I took the competition last year, and it worked. (Though I was really nervous about making that choice at the time.)

Second, structure is critically important. Not only is it allocated more possible points than any category except analysis, it also helps the grader understand the analysis better and can therefore lead to more points in that category, too. If two papers raise exactly the same arguments and counterarguments, the one that is structured more clearly will almost certainly get more analysis points than the other, in addition to the extra structure points. Additionally, having clear structure when writing the paper can show you, as the author, which arguments don't quite work and help you make them better.

Nearly all of the papers I graded had exactly the following headings:
I. Facts
II. Analysis
III. Conclusion

This is basically no help at all. It doesn't tell me anything about what the argument is and where it's going. I understand that it might be tempting to forgo subheadings because of the major space constraints, but they are totally worth it.