  Let BS(n_1,m_1) $\curvearrowright$ X_1 and BS(n_2,m_2) $\curvearrowright$ X_2
be two ergodic essentially free probability measure preserving actions of
nonamenable Baumslag-Solitar groups whose canonical almost normal abelian
subgroups act aperiodically. We prove that an isomorphism between the
corresponding crossed product II_1 factors forces BS(n_1,m_1) $\cong$
BS(n_2,m_2) when |n_1| $\neq$ |m_1| and BS(n_1,m_1) $\cong$ BS(n_2,$\pm$m_2)
when |n_1| = |m_1|. This improves an orbit equivalence rigidity result obtained
by Houdayer and Raum.
