This note proposes sufficient conditions under which a nonlinear system can be made Strongly iISS in the presence of actuator saturation. This property, recently proposed as a compromise between the strength of ISS and the generality of iISS, ensures boundedness of all solutions provided that the disturbance magnitude is below a certain threshold. We also show that, under a growth rate condition, the bounded feedback law proposed by Lin and Sontag for the stabilization of the disturbance-free system based on the knowledge of a control Lyapunov function, ensures Strong iISS in the presence of perturbations. We illustrate our findings on the angular velocity control of a spacecraft with limited-power thrusters.