Smooth Scrolling on ListBox

I'm using a ListBox styled like a StackPanel to display data.  The data is a list of objects, so each ListBoxItem is bound to an item.  Some ListBoxItems are very tall, others very short.

The ListBox scrolls an entire item at once.  There is no smooth scrolling.  So when a single ListBoxItem is taller than the height of the ListBox, I cannot read the entire item.  Scroll snaps to the next item.

I've placed a ScrollViewer around the ListBox to achieve smooth scrolling, but now clicking on a ListBox item that doesn't appear at the top is impossible.  For example, when I scroll to the last item and click on it, the ListBox jumps back to the top.

Any ideas?