ABSTRACT We propose an analytic model, CuspCore II, for the response of dark matter (DM) haloes to central gas ejection, as a mechanism for generating DM-deficient cores in dwarfs and high-z massive galaxies. We test this model and three other methods using idealized N-body simulations. The current model is physically justified and provides more accurate predictions than the earlier version, CuspCore I (Freundlich et al. 2020a). The CuspCore model assumes an instantaneous change of potential, followed by a relaxation to a new Jeans equilibrium. The relaxation turns out to be violent relaxation during the first orbital period, followed by phase mixing. By tracing the energy diffusion dE = dU (r), iteratively, the model reproduces the simulated DM profiles with ∼10 per cent accuracy or better. A method based on adiabatic invariants shows similar precision for moderate mass change, but underestimates the DM expansion for strong gas ejection. A method based on a simple empirical relation between DM and total mass ratios makes slightly inferior predictions. The crude assumption used in CuspCore I, of energy conservation for shells that encompass a fixed DM mass, turns out to underestimate the DM response, which can be partially remedied by introducing an alternative ‘energy’ definition. Our model is being generalized to address the differential response of a multicomponent system of stars and DM in the formation of DM-deficient galaxies.