different layout on one page

I would like to have a different layout on a particular page. In general I am using both sidebars, but in Single Post, I'd like to use the alternative layout that has a left-hand sidebar and no right-hand sidebar. The problem is that when I go to Widgets, I expected to see a new widget area for the left-hand sidebar, but I only see "main" and "third", same as before. I need to put a couple of widgets in the left-hand sidebar, but there doesn't seem to be any way of doing that.