In this paper, we introduce a new approach for joint segmentation, POS tagging and dependency parsing. While joint modeling of these tasks addresses the issue of error propagation inherent in traditional pipeline architectures, it also complicates the inference task. Past research has addressed this challenge by placing constraints on the scoring function. In contrast, we propose an approach that can handle arbitrarily complex scoring functions. Specifically, we employ a randomized greedy algorithm that jointly predicts segmentations, POS tags and dependency trees. Moreover, this architecture readily handles different segmentation tasks, such as morphological segmentation for Arabic and word segmentation for Chinese. The joint model outperforms the state-of-the-art systems on three datasets, obtaining 2.1% TedEval absolute gain against the best published results in the 2013 SPMRL shared task.