Overlapping speech is a common and relevant phenomenon in human conversations, reflecting many aspects of discourse dynamics. In this paper, we focus on the pragmatic role of overlaps in turn-in-progress, where it can be categorized as competitive or non-competitive. Previous studies on these two categories have mostly relied on controlled scenarios and small datasets. In our study, we focus on call center data, with customers and operators engaged in problem-solving tasks. We propose and evaluate an annotation scheme for these two overlap categories in the context of spontaneous and in-vivo human conversations. We analyze the distinctive predictive characteristics of a very large set of high-dimensional acoustic feature. We obtained a significant improvement in classification results as well as significant reduction in the feature set size.