I've got an ATI Radeon (not sure exact card; forgot to write it down when I left this morning; will update when I get back) and it is connected to an LG IPS237L 23" IPS LED monitor.
As you can seen in the xrandr output below, the resolution is currently set to 1920x1080. The monitor's information panel indicates this as well. The auto-adjustment is disabled as it's connected via HDMI, so the only thing I can really adjust is turning the over-scan on.
It helps a little, but the text is still blocky and the output doesn't extend to the end of the screen. It's almost as if 1920x1080 wasn't the monitor native resolution, but everything I've found on the monitor indicates that is the native resolution.
I'm using a DVI-HDMI cable, but that really shouldn't make any difference since they both use the same TMDS protocol. What am I missing here?