Left panel: WD 2047+372: observed variation of ⟨ B_z ⟩ and ⟨ | B | ⟩ fit by a simple dipolar model. Right panel: WD 2359-434: observed variation of ⟨ B_z ⟩ and ⟨ | B | ⟩ fit by a simple dipolar model (thin red lines), a co-linear dipole-quadrupole-octupole model (dashed black lines), and by a model including the superposition of a dipole with a non linear quadrupole (thick solid blue lines), as described in the text. Both FORS data (solid circles) and ESPaDOnS data (empty circles) have been used in the fits, with appropriate weights. The two oldest FORS1 data points are shown with nominal (but very uncertain) phases with open squares, but were not used in finding any of the models.