  Our goal is to visualize an additional data dimension of a tree with
multifaceted data through superimposition on vertical strips, which we call
columns. Specifically, we extend upward drawings of unordered rooted trees
where vertices have assigned heights by mapping each vertex to a column. Under
an orthogonal drawing style and with every subtree within a column drawn
planar, we consider different natural variants concerning the arrangement of
subtrees within a column. We show that minimizing the number of crossings in
such a drawing can be achieved in fixed-parameter tractable (FPT) time in the
maximum vertex degree $\Delta$ for the most restrictive variant, while becoming
NP-hard (even to approximate) already for a slightly relaxed variant. However,
we provide an FPT algorithm in the number of crossings plus $\Delta$, and an
FPT-approximation algorithm in $\Delta$ via a reduction to feedback arc set.
