MirageKnight: Unfortunately, I can't get the scrollbar to take a proper right-click. I may or may not be able to put a "grab handle" in there somewhere (like with Ger's bags) that will allow you move the window and get the right-click menu. While I'm working on it, I'd like to know: Would this work for you? Which corner do you want it in? And do you want it visible or just a clickable spot that you know is there?
Adder: The default location in the XML is puts the window's center at -106 pixels from the horizontal center and about 130 pixels from the top of the screen. Try the file I'm attaching here instead, I've moved it to be at the dead center of the screen by default. I can only hope it fixes it, because I honestly have no clue what the actual issue is.
Bachaco: I'll be adding the StayPut coding I came up with for the bag windows to the pet window, which will hopefully resolve the issue. (Not going to release until patch day, though, because the old pet commands won't work after then and the new ones won't work until then.

) And, thanks to the addition of the FrameControl property, it will now save all three states with the frame/titlebar settings while still allowing the frame visiblity to be controlled independently via the opacity sliders. Yay!
