We give a nearly-optimal algorithm for testing uniformity of distributions supported on \{-1,1\}^n, which makes \tilde O (\sqrt{n}/\varepsilon^2) queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)). The key technical component is a natural notion of random restriction for distributions on \{-1,1\}^n, and a quantitative analysis of how such a restriction affects the mean vector of the distribution. Along the way, we consider the problem of mean testing with independent samples and provide a nearly-optimal algorithm.