  In the year 2008 COMPASS recorded diffractive events of the signature
\pi^-(191 GeV) p --> X_fast p. We present results of the analysis of the
subsystems X = \eta(')\pi^-. Besides the known resonances a_2(1320), a_4(2040),
we study the properties of the spin-exotic P+ wave, and all other
natural-exchange partial waves up to spin J = 6. We find a striking difference
between the two final states: whereas the even partial waves J = 2, 4, 6 in the
two systems are related by phase-space factors, the odd partial waves are
relatively suppressed in the \eta\pi^- system. The relative phases between the
even waves appear identical whereas the phase between the D and P waves behave
quite differently, suggesting different resonant and non-resonant contributions
in the two odd-angular-momentum systems. Branching ratios and parameters of the
well-known resonances a_2 and a_4 are measured.
