Acoustic-prosodic entrainment describes the tendency of humans to align or adapt their speech acoustics to each other in conversation. This alignment of spoken behavior has important implications for conversational success. However, modeling the subtle nature of entrainment in spoken dialogue continues to pose a challenge. In this paper, we propose a straightforward definition for local entrainment in the speech domain and operationalize an algorithm based on this: acoustic-prosodic features that capture entrainment should be maximally different between real conversations involving two partners and sham conversations generated by randomly mixing the speaking turns from the original two conversational partners. We propose an approach for measuring local entrainment that quantifies alignment of behavior on a turn-by-turn basis, projecting the differences between interlocutors' acoustic-prosodic features for a given turn onto a discriminative feature subspace that maximizes the difference between real and sham conversations. We evaluate the method using the derived features to drive a classifier aiming to predict an objective measure of conversational success (i.e., low versus high), on a corpus of task-oriented conversations. The proposed entrainment approach achieves 72% classification accuracy using a Naive Bayes classifier, outperforming three previously established approaches evaluated on the same conversational corpus.