Different desktop with different dock? I'm using 10.7.4, and I use multiple desktops (in Spaces). When I switch between desktops, the dock does not change. 

I open an application in Desktop 1 and its icon remains in the dock after I switch to Desktop 2.

What I want is I open an application in Desktop 1, its icon remains in Desktop 1's dock, When I switch to Desktop 2, Desktop 2's dock only has application icons that I open in Desktop 2.

Is it possible to do that; to have different desktops with different docks?
Lion doesn't support that. It wasn't supported in Spaces under older versions of OS X, either.