Having taken the first set to a tie-break, Soderling fought back from 4-2 down in the second set to level at 4-4 but Nadal -- who lost to Andy Murray in the final last year -- showed no signs of the inconsistency that plagued the latter half of his 2009 campaign as he clinched victory.
And the 23-year-old, who lost to Andy Roddick in the semi-finals last year, dismissed concerns about his form despite struggling to find his best tennis since reaching the Australian Open final in January.
Aside from Byrd, the Bills are also attempting to re-sign left guard Andy Levitre, who is eligible to become a free agent after completing his four-year contract last season.