Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is based on the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of
 linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the HG framework and comparing the results with those of OT. We first describe the translation from Harmonic Grammars to systems solvable by linear programming algorithms. We then develop an HG analysis of ATR harmony in Lango that is, we argue, superior to the existing OT and rule-based treatments. We further highlight the usefulness of OT-Help, and the analytic power of HG, with a set of studies of the predictions HG makes for phonological typology.