We provide sharp bounds for the exponential moments and p-moments, 1 ≤ p≤ 2 , of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding extremal problem and reduce it to the already known Bellman function on BMO ([0 , 1]). In the case of tail estimates, a similar reduction does not work exactly, so we come up with a fine supersolution that leads to sharp tail estimates.