Automatically identifying the arguments of discourse connectives (e.g., and, because, however) is an important part of modeling discourse structure. Previous work used a single, general classifier for different connectives; however, connectives differ in their distribution and behavior, so conflating them this way loses discriminative power. Here, we show that using models for specific connectives and types of connectives and interpolating them with a general model improves performance. We also describe additional features that provide greater sensitivity to morphological, syntactic, and discourse patterns, and less sensitivity to parse quality. Our best model achieves a 3.6% absolute improvement over the state-of-the-art on identifying both arguments of discourse connectives when using features from gold-standard parses, and a 9.0% improvement when using automatically produced parses.