  We study dual conformal transformations of minimal area surfaces in $AdS_5
\times S^5$ corresponding to holographic smooth Wilson loops and some other
related observables. To act with dual conformal transformations we map the
string solutions to the dual space by means of T-duality, then we apply a
conformal transformation and finally T-dualize back to the original space. The
transformation maps between string solutions with different boundary contours.
The boundary contours of the minimal surfaces are not mapped back to the AdS
boundary, and the regularized area of the surface changes.
