  We have studied the angular dependence of the irreversible magnetization of
several YBa$_2$Cu$_3$O$_7$ and 2H-NbSe$_2$ single crystals with columnar
defects tilted off the c-axis. At high magnetic fields, the irreversible
magnetization $M_i(\Theta_H)$ exhibits a well known maximum when the applied
field is parallel to the tracks. As the field is decreased below $H \sim 0.02
H_{c2}$, the peak shifts away from the tracks' direction toward either the
c-axis or the ab-planes. We demonstrate that this shift results from the
misalignment between the external and internal field directions due to the
competition between anisotropy and geometry effects.
