  We study the delocalization by bulk randomness of a single flux line (FL)
from an extended defect, such as a columnar pin or twin plane. In three
dimensions, the FL is always bound to a planar defect, while there is an
unpinning transition from a columnar pin. Transfer matrix simulations confirm
this picture, and indicate that the divergence of the localization length from
the columnar defect is governed by a liberation exponent $\nu_\perp =1.3 \pm
0.6$, for which a ``mean-field'' estimate gives $\nu_\perp \approx 0.78$. The
results, and their extensions, are compared to other theories. The effects may
be observable in thin samples close to $H_{c1}$.
