Dominantly or predominantly?

I think the 2013 Revised Rules of Civil Procedure, as proposed, will do a lot in speeding up our court processes. Let's see if I can cite specific examples in a future post.

While going over the Primer on the proposed rules  I stumbled over this passage on page 2:

It seems out of place even at first glance. Although dominantly and predominantly are synonymous, they have a subtle difference that could make the sentence stilted such as in this case.

So, when does one use dominantly over predominantly? Here's from Yahoo! Answers:

Ok, then, which word do we come across more which make it predominant over the other?

A Google search of the phrase "dominantly adversarial system" yields this:

The 1st, 2nd, and 3rd entries all refer to same primer. The second entry actually also uses "predominantly" which was truncated:

http://law.wisc.edu/alumni/gargoyle/archive/23_4/gargoyle_23_4_3.pdf

What about a search for "predominantly adversarial system"? Here's the result: