Light-like polygonal super-Wilson loops are dual to scattering amplitudes in planar N=4 super-Yang-Mills and enjoy an infinite-dimensional Yangian symmetry which extends the superconformal symmetry.  However, this symmetry is anomalous.  In this talk we will describe a super-Wilson loop on a smooth contour, which is free of UV divergences and on which the superconformal symmetry operators are not anomalous.  We also study the action of level one Yangian generators on the one-loop expectation value of this super-Wilson loop. [This is work in progress with N.Beisert, D.Muller and J.Plefka]