  Tree trace reconstruction aims to learn the binary node labels of a tree,
given independent samples of the tree passed through an appropriately defined
deletion channel. In recent work, Davies, R\'acz, and Rashtchian used
combinatorial methods to show that $\exp(\mathcal{O}(k \log_{k} n))$ samples
suffice to reconstruct a complete $k$-ary tree with $n$ nodes with high
probability. We provide an alternative proof of this result, which allows us to
generalize it to a broader class of tree topologies and deletion models. In our
proofs, we introduce the notion of a subtrace, which enables us to connect with
and generalize recent mean-based complex analytic algorithms for string trace
reconstruction.
