Is there any way to get globalCompositeOperation copy work like it does in Chrome, but in Firefox/Opera?

Question

Trying to free-hand draw on a canvas without having opacity 1, however it turns out like this: http://i.imgur.com/ONhSlhV.png

Setting globalCompositeOperation to copy solves it, however in Firefox/Opera copy clears the entire canvas before drawing, unlike how it does it in Chrome. I know another solution is to redraw all the lines as one before applying stroke every time you draw, however it's quite the performance hit just to get opacity to work.