"Brittney does not expect any miracles to happen but hopes that the appeal court will hear the arguments of the defense and reduce the term," her lawyers said in a statement.
The U.S. and Russia are trying to work out a prisoner exchange that involves basketball star Brittney Griner. While they've done deals for decades, the trading usually involves spies for spies.
Bout is a Russian who was the world's most notorious arms dealer in the 1990s and early 2000s. He's serving a 25-year prison sentence in Illinois, but could be freed as part of a U.S.-Russia swap.