The lexical items 'like' and 'well' can serve as discourse markers (DMs), but can also play numerous other roles, such as verb or adverb. Identifying the occurrences that function as DMs is an important step for language understanding by computers. In this study, automatic classifiers using lexical, prosodic/positional and sociolinguistic features are trained over transcribed dialogues, manually annotated with DM information. The resulting classifiers improve state-of-the-art performance, at about 90% recall and 79% precision for like (84.5% accuracy, kappa = 0.69), and 99% recall and 98% precision for well (97.5% accuracy, kappa = 0.88). Automatic feature analysis shows that lexical collocations are the most reliable indicators, followed by prosodic/positional features, while sociolinguistic features are marginally useful for the identification of DM like. The differentiated processing of each type of DM improves classification accuracy, suggesting that these types should be treated individually.