Tooltips in GTK apps

This is not suse-specific, but something that's really annoying me, and maybe some others here. I run KDE, but I often use Firefox and Thunderbird. Does anyone know any way to turn off tooltips for these? I've not found anything in the apps themselves or in gnome-control-center. The biggest problem is Thunderbird, which will raise a tooltip if you leave the cursor in the subject/from/etc list. If I then switch desktops (which I do from the keyboard), the tooltip will remain on the screen for some time, even though I'm on a new desktop, which is rather ugly.