Maintaining information in context is essential in successful real-time language comprehension, but maintenance is cognitively costly and can slow processing. We hypothesize that rational language users selectively maintain information that is crucial for future prediction, guided by syntactic structure. Under this view, two factors affect maintenance cost: the number of predicted heads and the number of incomplete dependencies. Although these factors have been treated as competing hypotheses in the literature, our account predicts that they are not reducible to one another. We show this is the case in a naturalistic reading time dataset in Japanese, a language in which the two factors contrast particularly clearly. We further show that there is a tradeoff such that readers that slow down for maintenance tend to benefit more from predictability, providing additional support for the proposed account. These patterns are not evident in English, however, and we highlight some issues to be resolved to understand the contribution of syntax in memory-efficient processing of various languages.