Maybe you misunderstood something, I didn't unsdertood the question... or the problem is not in the overflow settings.
Overflow: auto will add the scrollbar only if needed (content bigger than container).
Òverflow: visible will add the scrollbar.
Òverflow: hidden will NOT add the scrollbar.
I understand that you want the x-content to be hidden, so overflow-x: hidden, but from your question it seems to me that don't want the vertical scrollbar to see the vertically overflowed content.
Maybe the problem is that is set a fixed height (or max-height) for the container and the content is bigger. Remove the height (or max height) and you'll avoid the vertical scrollbar.
...or as maybe I said, just didn't understood what is the desired effect.
