Thickness modulation at the edges of nanostructured magnetic thin films is shown to have important effects on their perpendicular magnetic anisotropy. Thin film wires with tapered edges were made from [Co/Pd]20 multilayers or L10-FePt films using liftoff with a double layer resist. The effect of edge taper on the reversal process was studied using magnetic force microscopy and micromagnetic modeling. In [Co/Pd]20 the anisotropy was lower in the tapered edge regions which switched at a lower reverse field compared to the center of the wire. The L10-FePt wires showed opposite behavior with the tapered regions exhibiting higher anisotropy. ; Comment: 15 pages, 6 figures