Consider Bernoulli bond percolation on an infinite transitive graph. A classical result states that for each p < p_c, the probability that a given vertex belongs to a component of size at least n decays exponentially in n. Sahar Diskin, Ritvik Ramanan Radhakrishnan, Benny Sudakov, Vincent Tassion, and I have recently proved the analogous result for p > p_c.