A previously proposed energy criterion for predicting the conditional stability of incompressible flows, which is based on properly defined generalized energies, is considered. An extension of the procedure for the construction of generalized energies is proposed here, leading to the definition of a broader class of generalized energies which may depend on several free parameters. The optimal free parameters are computed by searching the value for which the energetic stability criterion predicts the maximum critical L 2 energy. The capabilities of the resulting stability criterion are appraised through the application to low-dimensional non-linear quadratic models, mimicking the subcritical instability behavior of particular incompressible flows. Many shear flows are characterized by a subcritical instability regime, in which the stability of the base flow is guaranteed only if the initial amplitude of a given disturbance is lower than a critical threshold value. This value is a decreasing function of Re between Reg and ReL , ReL being the critical Reynolds number predicted by linear stability and Reg being the Reynolds number of global stability, i.e., for Re < Reg all disturbances, whatever their initial amplitude, decay asymptotically in time. In several cases, the classical energetic stabil- ity theory does not give any useful information concerning the subcritical regime, since it predicts a critical Reynolds number (ReE ) which is significantly lower than Reg. As discussed in the literature, this failure is mainly due to two major flaws. First, the non-normality of the linearized Navier-Stokes (NS) operator leads to the well-known transient growth of the disturbance energy, which eventually may decrease to zero, while the energetic criterion requires the disturbance energy to decrease monotonically in time. Second, for many flows, the nonlinear part of the NS operator and, consequently, the amplitude of the disturbance do not play a role in the computation of ReE . An energetic criterion was proposed in (1) in which the problems related to the non-normality of the linear operator are bypassed and the amplitude of the disturbance is taken into account in the problem. This criterion is based on a procedure which consists of two main steps. First, a generalized energy is defined through a perturbation of the classical L 2 energy, which is aimed at overcoming the non-normality of the linearized operator. Indeed, the metric perturbation is such that the time variation of the generalized energy due to the linear term of the disturbance evolution equation is negative definite. Second, by imposing the monotonic decay of the generalized energy, a criterion of conditional stability is obtained for each Reynolds number up