The effect of graded anisotropy on static and dynamic magnetic properties of Ar+-irradiated FePt films has been investigated by static magnetometry, magnetic force microscopy, and Brillouin light scattering from thermally excited spin waves. A gradual variation of magnetic anisotropy with film thickness was obtained by Ar+ irradiation. The irradiation incidence angle influences the anisotropy profile: on decreasing α, a decreasing thickness of the hard L10 phase and an increasing thickness of the soft A1 phase were obtained. Accordingly, the zero-field spin-wave frequency gap was found to decrease. In the sample with the highest soft-phase thickness the spin-wave frequency gap takes a substantial value (ν0≈6 GHz), which could be reproduced assuming the presence of a nonzero "rotatable" anisotropy (i.e., any direction in the film plane can be established as the easy axis by the application of a saturating magnetic field along this direction). The hypothesis is supported by both magnetometry and magnetic force microscopy data.