Some fluid mechanical systems exhibit transition to non-trivial flows even when the base state is linearly stable. In such cases, it is believed that although all infinitesimal perturbations about the base state decay, perturbations of finite size may grow. At the same time, there are energy methods which prove monotonic decay of every perturbation in some parts of the parameter space. I will present an extension of these energy stability methods to determine thresholds on the size of perturbations that may grow. This extension helps us to systematically study the way in which nonlinearities may play a role. I will demonstrate this method using some toy models.