Confused about material texture slots New to Blender and I have done some basic modelling and painting textures on. In general that has gone well. One specific thing I want to do is copy a textured object so I can make some variation of it.

I thought this would be a routine operation but cannot find a way. When I duplicate the object the new and old share the same material and the texture slot linked to it. So if I paint one it also paints the other. 

I can give a new material but I cannot link a copy of the texture to branch from.  I've tried changing Blender preferences to not link material/textures when duplicating. Tried settings users of the texture slot's associated image file's users to single user, and also changing the material between the object's data and object's object data but nothing has achieved what I want.

I know I could save a new blender file and work in that for variations but I want these objects in the one scene.
Make sure your image texture and your material are single users, if anything is repercuted on the other objects it means they are still using the same data-block.