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Neural models at the sentence level often operate on the constituent words/tokens in a way that encodes the inductive bias of processing the input in a similar fashion to how humans do. However, there is no guarantee that the standard ordering of words is computationally efficient or optimal. To help mitigate this, we consider a dependency parse as a proxy for the inter-word dependencies in a sentence and simplify the sentence with respect to combinatorial objectives imposed on the sentence-parse pair. The associated optimization results in permuted sentences that are provably (approximately) optimal with respect to minimizing dependency parse lengths and that are demonstrably simpler. We evaluate our general-purpose permutations within a fine-tuning schema for the downstream task of subjectivity analysis. Our fine-tuned baselines reflect a new state of the art for the SUBJ dataset and the permutations we introduce lead to further improvements with a 2.0% increase in classification accuracy (absolute) and a 45% reduction in classification error (relative) over the previous state of the art.