Markov logic networks (MLNs) are an expressive representation for statistical relational learning that generalizes both first-order logic and graphical models. Existing methods for learning the logical structure of an MLN are not discriminative; however, many relational learning problems involve specific target predicates that must be inferred from given background information. We found that existing MLN methods perform very poorly on several such ILP benchmark problems, and we present improved discriminative methods for learning MLN clauses and weights that outperform existing MLN and traditional ILP methods.