Traditional Markov network structure learning algorithms perform a search for globally useful features. However, these algorithms are often slow and prone to finding local optima due to the large space of possible structures. Ravikumar et al. recently proposed the alternative idea of applying L1 logistic regression to learn a set of pairwise features for each variable, which are then combined into a global model. This paper presents the DTSL algorithm, which uses probabilistic decision trees as the local model. Our approach has two significant advantages: it is more efficient, and it is able to discover features that capture more complex interactions among the variables. Our approach can also be seen as a method for converting a dependency network into a consistent probabilistic model. In an extensive empirical evaluation on 13 datasets, our algorithm obtains comparable accuracy to three standard structure learning algorithms while running 1-4 orders of magnitude faster.