Nodes in a binary search tree that span a range

Question

I have a binary search tree of height $h$ with an integer in each leaf. I also have a range $[\ell,u]$. I want to find a set of nodes that span the range $[\ell,u]$, i.e., a set $S$ of nodes such that the leaves under $S$ form all (and only) those leaves containing integers in the range $[\ell,u]$. How large does $S$ need to be, in the worst case, as a function of the height $h$? How do I find such a set explicitly?