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The Bureau of Labor Statistics says the unemployment rate for the latest generation of veterans fell to less than 10 percent last year. That's down from more than 12 percent in 2011. About a third of all post-9/11 veterans served in Iraq, Afghanistan, or both.

Brian Wilson is with the Lone Star Veterans Association, a Houston non-profit that helps younger vets find work.

"In December 2011, we did a quick survey among our members, and we just asked, 'Are you employed? Unemployed? Part-time? Full-time?' And we had about 22 percent of the people say that they were looking for work.

"And then in December 2012, just this last this year, we asked this same question to our membership. And that number dropped to 16 percent, which is just amazing, because it shows that the work that we've been doing over the past year actually did have an impact on our veterans."

But the picture is bleaker for the youngest veterans, age 24 and under. The BLS report shows nearly one in five was unemployed last year.