  We give an elementary proof for Lewis Bowen's theorem saying that two
Bernoulli actions of two free groups, each having arbitrary base probability
spaces, are stably orbit equivalent. Our methods also show that for all compact
groups K and every free product \Gamma of n infinite amenable groups, the
factor K^{\Gamma}/K of the Bernoulli action of \Gamma on K^{\Gamma} by the
diagonal action of K, is isomorphic with a Bernoulli action of \Gamma.
