Abstract Counting the models of a propositional formula is a key issue for a number of AI problems, but few propositional languages offer the possibility to count models efficiently. In order to fill the gap, we introduce the language EADT of (extended) affine decision trees. An extended affine decision tree simply is a tree with affine decision nodes and some specific decomposable conjunction or disjunction nodes. Unlike standard decision trees, the decision nodes of an EADT formula are not labeled by variables but by affine clauses. We study EADT, and several subsets of it along the lines of the knowledge compilation map. We also describe a CNF-to-EADT compiler and present some experimental results. Those results show that the EADT compilation-based approach is competitive with (and in some cases is able to outperform) the model counter Cachet and the d-DNNF compilationbased approach to model counting.