In this paper we propose a method to redesign given controllers for systems with input saturation. In contrast to typical approaches, we do not saturate the output of the controller and we do not rely on anti-windup compensators. Instead, we reformulate required bounds on the input as constraints on the controller state and we formulate redesign objectives such that adjusted controllers satisfy the required constraints. Particularly, we focus on redesigning existing controllers in a way that the associated dissipation property is preserved, allowing for a straightforward adaptation of existing stability results. This makes the suggested method particularly suitable for nonlinear systems, where the overall stability often relies on the existence of certain dissipation properties. To demonstrate the proposed methodology, we redesign a popular distributed controller aiming at power sharing in electricity networks such that the new controllers additionally satisfy important transient constraints.