  Previous work showed that every pair of nontrivial Bernoulli shifts over a
fixed free group are orbit equivalent. In this paper, we prove that if
$G_1,G_2$ are nonabelian free groups of finite rank then every nontrivial
Bernoulli shift over $G_1$ is stably orbit equivalent to every nontrivial
Bernoulli shift over $G_2$. This answers a question of S. Popa.
