View Height / Using Ti.UI.FILL without overly enlarging containing view

I have a scenario like this:

<View id="containingView" height="Ti.UI.SIZE" width="Ti.UI.FILL>
    <View id="thinLine" height="Ti.UI.FILL"  width="1px" left="20" />
    <View id="miscOtherContent" height="Ti.UI.SIZE" left="40" />
</View>

I wish for the height of the "containingView" to be determined by "miscOtherContent". But instead "thinLine" is making the "containingView" much larger than it has to be. Any ideas?