  We demonstrate the applicability of the dressing method to the problem of
constructing new classical solutions for Euclidean worldsheets in anti-de
Sitter space. The motivation stems from recent work of Alday and Maldacena, who
studied gluon scattering amplitudes at strong coupling using a generalization
of a particular worldsheet found by Kruczenski whose edge traces a path
composed of light-light segments on the boundary of AdS. We dress this `giant
gluon' to find new solutions in AdS_3 and AdS_5 whose edges trace out more
complicated, timelike curves on the boundary. These solutions may be used to
calculate certain Wilson loops via AdS/CFT.
