In several applications, one is interested in a detailed description of steady states of hyperbolic balance laws. Unfortunately, such steady equilibria are rarely known in closed-form. This is the main reason why the exact (up to machine precision) capturing of such analytical solutions, as well as their small-perturbation-analysis, is typically very expensive from a numerical point of view, requiring very high levels of refinement with associated employment of huge computational resources. In order to overcome such a serious issue, several so-called “fully well–balanced” strategies have been proposed, able to exactly capture analytical steady states. In this work [1], we propose some novel (arbitrarily) high order continuous interior penalty stabilizations for Continuous Galerkin/Residual Distribution schemes for the Shallow Water equations. All of them are designed in such a way to exactly capture the lake at rest steady state. However, some of those, based on the notion of space residual, address the challenge of preserving generic steady equilibria, whose analytical expression is not known. The good properties of the proposed stabilizations are confirmed on a wide variety of tests. Many of the presented ideas can be applied to generic hyperbolic systems of balance laws, e.g., the Euler equations with gravitation.