Cannot hiding vertical scrollbar on CListCtrl (reappears when scrolling)

I have a CSplitterWnd control that contains two (ownerdraw) CListCtrls. I would like to hide the vertical scrollbars on both ListCtrls so that the CSplitterWnd scrollbar controls scrolling in both ListCtrls.
I cannot seem to hide (or even remove) the scrollbars from the ListCtrls. I have tried everything from setting/removing various windows styles (ie. ~WS_VSCROLL) and calling various functions such as ShowScrollBar(SB_VERT, FALSE).

When I do manage to hide the scrollbar (with a some hacking) it re-appears when the ListCtrl window is scrolled (using the cursor keys or with the CSplitterWnd scrollbar).