$P$ is an embedded subtree of $T$ if $P$ can be obtained by deleting some nodes from $T$: if a node $v$ is deleted, all edges adjacent to $v$ are also deleted, and outgoing edges are replaced by edges going from the parent of $v$ (if it exists) to the children of $v$. Deciding whether $P$ is an embedded subtree of $T$ is known to be NP-complete. Given two trees (a target $T$ and a pattern $P$) and a natural number $w$, we address two problems: 1. counting the number of windows of $T$ having height exactly $w$ and containing pattern $P$ as an embedded subtree, and 2. counting the number of slices of $T$ having height exactly $w$ and containing pattern $P$ as an embedded subtree.