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To date, few attempts have been made to develop new methods and validate existing ones for automatic evaluation of discourse coherence in the noisy domain of learner texts. We present the first systematic analysis of several methods for assessing coherence under the framework of automated assessment (AA) of learner free-text responses. We examine the predictive power of different coherence models by measuring the effect on performance when combined with an AA system that achieves competitive results, but does not use discourse coherence features, which are also strong indicators of a learner's level of attainment. Additionally, we identify new techniques that outperform previously developed ones and improve on the best published result for AA on a publically-available dataset of English learner free-text examination scripts.