Algorithms for signal recovery in compressed sensing (CS) are often improved by stabilization techniques, such as damping, or the less widely known so-called fractional approach, which is based on the expectation propagation (EP) framework. These procedures are used to increase the steady-state performance, i.e., the performance after convergence, or assure convergence, when this is otherwise not possible. In this paper, we give a thorough introduction and interpretation of several stabilization approaches. The effects of the stabilization procedures are examined and compared via numerical simulations and we show that a combination of several procedures can be beneficial for the performance of the algorithm.