Mental illness is one of the most pressing public health issues of our time. While counseling and psychotherapy can be effective treatments, our knowledge about how to conduct successful counseling conversations has been limited due to lack of large-scale data with labeled outcomes of the conversations. In this paper, we present a large-scale, quantitative study on the discourse of text-message-based counseling conversations. We develop a set of novel computational discourse analysis methods to measure how various linguistic aspects of conversations are correlated with conversation outcomes. Applying techniques such as sequence-based conversation models, language model comparisons, message clustering, and psycholinguistics-inspired word frequency analyses, we discover actionable conversation strategies that are associated with better conversation outcomes.