This paper is about gate sizing under a statistical delay model. It shows we can solve the gate sizing problem exactly for a given statistical delay model. The formulation used allows many different forms of objective functions, which could for example directly optimize the delay uncertainty at the circuit outputs. We formulate the gate sizing problem as a nonlinear programming problem, and show that if we do this carefully, we can solve these problems exactly for circuits up to a few thousand gates using the publicly available large scale nonlinear programming solver LANCELOT.