  A sample of 35,000 events of the type pi-p --> eta'pi-p_slow (eta' --> eta
pi-pi+, eta --> gamma gamma) with -t>0.1 GeV^2/c^2 was selected from COMPASS
2008 data for a partial-wave analysis. We study the broad P_+ structure known
from previous experiments at lower energies, in particular its phase motion
relative to the D_+-wave near the a_2(1320) mass and relative to a broad
D_+-wave structure at higher mass. We also find the a_4(2040). We compare
kinematic plots for the eta'pi^- and eta pi- final states.
