# Line at edge of transparent texture on XNA mesh

I have a mesh that is computer generated with a texture on top of it with transparancy on one side. The SamplerState is set to LinearWrap because I would like the texture to wrap. The problem I have is that this transparent edge has some weird aliasing. This does not occur when I set the SamplerState to LinearClamp.

I found that when letting the U coordinate go from 0.1 to 0.9 this does not happen. Probably on the transparent side it interpolates U coordinate 1 with U coordinate 0.

What could be the solution to prevent aside from not letting the U coordinate go all the way to 1?

mySampler.Filter = TextureFilter.Linear;