Enumerative coding for tree sources is not straightforward, since the 
size of the type class of a sequence $x^n$ with respect to a given tree 
may deviate significantly from $exp(n \hat{H}(x^n))$, where $\hat{H}(x^n)$ 
is the empirical entropy of $x^n$ with respect to the model. The latter
asymptotic behavior is key to twice-universal enumerative schemes for 
FSM sources, including fully parametrized $k$-th order Markov models. 
We survey recent work on the characterization of type classes of tree 
models, and describe an enumerative coding scheme that is twice-universal 
in the class of tree sources in the sense that, for a string emitted by 
an unknown tree source, the expected normalized codelength of the encoding 
approaches the entropy rate of the source with a covergence rate 
(K/2)(log n)/n, where K is the number of free parameters of the tree. 
The encoding consists of the index of the sequence in a type class 
related to the tree, and an efficient description of the class itself. 
It is also shown that there is some freedom in the choice of the class 
partition used in the encoding, and that variations in the size of the 
class are compensated by offsetting variations in the length of the 
description of the class, maintaining the universality result.