hmmm the boxes idea looks clear. Though I'm a bit anxious about it since it might have some side effects on the other graphics I have in the plot - notches eg. (which for reference looks like: http://i54.tinypic.com/k9hoom.png )
I think the problem lies with the ways lines are printed. Also a random line:
x = 1:10; y=rand(10,1);l= line(x,y,'LineWidth',32);
Thinking about this I came up with an idea. If I'd put dot markers on all corners it should cover the "shame". They'd just have to be the same size as the line. I'm just experimenting with that.