Using data from Nintemann et al. (2020), we explore the variability in complexity and informativity across spatial demonstrative systems using spatial deictic lexicons from 223 languages. We argue from an information-theoretic perspective (Shannon, 1948) that spatial deictic lexicons are efficient in communication, balancing informativity and complexity. Specifically, we find that under an appropriate choice of cost function and need probability over meanings, among all the 21146 theoretically possible spatial deictic lexicons, those adopted by real languages lie near an efficient frontier. Moreover, we find that the conditions that the need probability and the cost function need to satisfy are consistent with the cognitive science literature regarding the source-goal asymmetry. We also show that the data are better explained by introducing a notion of systematicity, which is not currently accounted for in Information Bottleneck approaches to linguistic efficiency.