What information from an act of sentence understanding is robustly represented in the human brain? We investigate this question by comparing sentence encoding models on a brain decoding task, where the sentence that an experimental participant has seen must be predicted from the fMRI signal evoked by the sentence. We take a pre-trained BERT architecture as a baseline sentence encoding model and fine-tune it on a variety of natural language understanding (NLU) tasks, asking which lead to improvements in brain-decoding performance. We find that none of the sentence encoding tasks tested yield significant increases in brain decoding performance. Through further task ablations and representational analyses, we find that tasks which produce syntax-light representations yield significant improvements in brain decoding performance. Our results constrain the space of NLU models that could best account for human neural representations of language, but also suggest limits on the possibility of decoding fine-grained syntactic information from fMRI human neuroimaging.