  Recently, Adrian Ioana proved that all crossed products by free ergodic
probability measure preserving actions of a nontrivial free product group
\Gamma_1 * \Gamma_2 have a unique Cartan subalgebra up to unitary conjugacy.
Ioana deduced this result from a more general dichotomy theorem on the
normalizer N_M(A)'' of an amenable subalgebra A of an amalgamated free product
von Neumann algebra M = M_1 *_B M_2. We improve this dichotomy theorem by
removing the spectral gap assumptions and obtain in particular a simpler proof
for the uniqueness of the Cartan subalgebra in crossed products by \Gamma_1 *
\Gamma_2.
