Ubuntu – How to open two half-screen windows in a row without overlapping

I use a monitor that is exactly 2×1024 pixels wide as a substitute for a dual-screen configuration.

In Ubuntu 10.10, I could open two windows in a row and each would be automatically placed on a different half of the screen, like this:

In Ubuntu 11.04, the launcher introduces a displacement in the default location for new windows that causes them to encroach upon the other half of the screen. The resulting default behavior is now to create an overlap of the two windows:

This is senseless. How can I restore the normal behavior?

Also, I would like to preempt the suggestion that I simply shorten the default width of windows to accommodate the for the launcher. Firstly, this defeats the purpose of having purchased a monitor this wide in the first place; 1024 pixels is an important minimum width to meet because many popular websites are designed for this size and will display horizontal scroll bars if the windows are smaller:

More importantly, though, is that I frequently use the default Grid plugin in Compiz to move windows from one half of the screen to the other. This action automatically resizes windows to half of the screen width, so my narrower widths would quickly be overridden.