  The definition of $k^{th}$-order empirical entropy of strings is extended to
node labelled binary trees. A suitable binary encoding of tree straight-line
programs (that have been used for grammar-based tree compression before) is
shown to yield binary tree encodings of size bounded by the $k^{th}$-order
empirical entropy plus some lower order terms. This generalizes recent results
for grammar-based string compression to grammar-based tree compression.
